Mary invites the Solomons on a murder mystery weekend, thinking that it might prove a fun activity. However, she goes down with food poisoning and retreats upstairs to her room. Downstairs, meanwhile, the Solomons are horrified when the first murder takes place, believing it to be real and, annoyed at the apparent lackadaisical efforts of Scotland Yard detective "Inspector McAffrey", they decide to try to solve the mystery themselves.

Mary reveals to Dick that she has been observing his family for a number of years and that she would like to make a documentary about them, in order to show how the 'typical American family' has changed. Unfortunately, Mary's film soon begins to create tension among the family and accusations that Dick is an abusive father, Tommy is a bed-wetter and Sally is secretly a lesbian start flying around, so Harry decides to become an alcoholic so as not to be left out.

The Solomons are struggling to take in the news - they have been ordered back home due to Dick's transgression with Liam. Dick's first instinct is to ask Mary to come, so he takes her to the planetarium before breaking the news to her that they are leaving, and asking her if she will join them. Meanwhile, since admitting his fear to Sally, Don has decided to quit the police force and open a muffin store, but Sally is disgusted by this career choice and decides to whip Don into shape - and turn him into a hardy police officer. At home, Harry and Tommy are attempting to organize a farewell party for the aliens, but have no money, so they decide to max out their credit cards and not worry about paying the bill, since they'll be halfway across the galaxy - they even hire Elvis Costello to sing Fly Me to the Moon.

After three years, the Big Giant Head has finally accepted Sally's request to have her body changed for a man's. For their convenience, the bodies of Dick and Sally are switched. Now, in each other's bodies, Dick and Sally must try and maintain each other's romantic relationships and get accustomed to the changes that their new gender brings, while waiting for their request to be switched back to be accepted. Meanwhile, Harry is left in charge of Happy Doug's when Doug goes on vacation, but becomes worried when a group of burly, tough-looking bikers arrive.

An invitation arrives in the mail from an 'Aunt Florence', inviting 'Richard Solomon' to attend a Solomon family reunion in Indiana. This is obviously a mistake, so Dick phones Florence to set the record straight. Upon discovering that Richard is so estranged that his family wouldn't recognize him anyway, he decides that the aliens could do with some roots and accepts the invitation. Upon arriving, however, it becomes clear that the only reason the real Richard is estranged is because of an old family fallout - and it hasn't burned out yet.

Dick decides that the Solomons don't “fit in” on Earth, so he shops for an ethnic group to join. Meanwhile, Sally wants to fit in with Tommy's handsome teacher.

The Solomons discover a brand of new collectibles called Fuzzy Buddies (a parody of Beanie Babies) when eating at a fast food diner, and Dick soon becomes so obsessed with collecting them that he begins to lose control of his family's finances. Tommy's coach is annoyed at his lack of team 'pep' and so makes him the school mascot - a giant owl called Hootie. Things goes wrong, however, when Tommy becomes so high on school pep that he attacks the coach.

Tommy is still reeling from his breakup with Alissa, but Sally and Harry convince him that if he can find an excuse to go over to her house, he can persuade her to watch a movie with him. When the pair leave the house together, however, Strudwick is suspicious and confronts Dick. Mrs. Dubcek suggests that they could have eloped, so Dick and Strudwick rush off to track them down before there's a baby on the scene, managing to accidentally abandon Mary in the process. Meanwhile, Tommy has rented a scary movie to watch with Alissa, in the hope that it might bring her into his arms, but Sally and Harry decide to show up and make it more real.

Mary is having trouble dealing with what she has just seen - Dick transforming Liam into a monkey, which he had done to stop him doing the same to the Earth's population. Dick consults the other Solomons and they decide that the best approach is to deny everything. Meanwhile, Mary meets with Nina and Judith, who confess that they believe Dick to be an international terrorist, so when Dick and Mary next meet, she demands that he tell her the truth about himself. So, Dick tells Mary that he and the others are aliens. Mary's reaction is first disbelief, then shock, and then she finds it sexy to be dating a spaceman. Elsewhere, the local store has been robbed and Sally catches Don hiding in the frozen foods freezer, where he admits that he hid because he was scared. Harry takes a different line and asks the shopkeeper Sam out on a date, but later runs into her working at a posh restaurant, where she instructs him to call her Samantha. Confused, Harry believes that he is dating twins.

Dr. Albright finally agrees to date Dick and Harry receives an ominous message from the home planet.

Thanksgiving's an alien concept for the Solomons; it's an annoyance for Sally (who must cook), and an onus on Tommy. But Harry finds romance.

Harry and Vicki prepare for an evening of amour. Then Vicki's jealous ex crashes the party. Meanwhile, Tommy "comes out" as a gourmet chef.

Dick realizes that he doesn't know how to use a computer and strives to learn how to use one. When he does it takes over his life and he becomes a recluse. Sally and Tommy decide to do away with their old TV in favor of a newer, better one, but end up becoming addicted, wanting all the latest features. Harry and Vicki, however, are trying to get pregnant, but the medical-science part of it is turning Harry off.

Dick is jealous when fellow physics professor Vincent Strudwick publishes a critically acclaimed, bestselling book on physics, and, while Mary busies herself showing the visiting Nobel Prize winners around the campus, he decides to write a second book that will better Strudwick's. He then realizes, however, that he cannot publish all the secrets of the universe without raising unwanted questions, and so looks for another way to get at Strudwick, using Tommy and Alissa - who, it turns out, is Strudwick's daughter. Sally and Don decide to start hanging out as friends, but soon find themselves unable to resist each other.

When an obnoxious professor dies during a party in his honor, Dick finds the will specifies that he must deliver a “forthright and honest” eulogy about the universally despised academic. Tommy neglects his female pal August to hit it off with an “easy” cheerleader.

A snowstorm -- the Solomons' first -- spoils Dr. Albright's trip to Chicago, leaving her stranded in a truck stop with Dick.

Homecoming's upcoming, but Dick can't seem to understand football's appeal. Tommy has a crush on his Glee Club teacher. Sally makes Nina her best friend. Harry gets a job as a security officer.

Dick's delighted (but Tommy isn't) when Tommy's accepted to a school for smart kids. Sally falls for a guy she met in a gay bar. Harry dabbles in magic.

Sally discovers the joys of motherhood when Mrs. Dubcek asks the Solomons to baby-sit her grandson. Meanwhile, Dick begs Mary to let him “fish sit” for her while she’s away at a conference.

Dick, upset that Mary got a prime parking space and he didn't, quits his job. Harry loses his memory and becomes paranoid thinking aliens are taking over the world.

Albright derides the Solomons as "weird," so Dick decides to make them "average."

Conclusion. Dick has a rival for the title of Pendelton's nuttiest professor with the arrival of the mysterious Dr. Liam Neesam. Meanwhile, Sally thinks she's losing her touch with men.

Dick tapes a promotional video for Pendelton; Don gives Sally a key to his apartment; and Nina and Harry find each other.

When Playpen magazine arrives at Pendleton, looking for students to pose nude, Sally decides to take part. While Dick encourages this, Don is furious. Dick is horrified when he discovers that Mary posed nude for an art shoot twenty years ago, and tracks down the photographer. Harry decides to test if clothes are "all a big scam" by becoming a nudist. Tommy has his eyes on his new lab partner, Alissa Strudwick.

When Harry's boss Doug starts deducting income tax from Harry's paycheck, the Solomons realize that they have never filed a tax return and that they owe $9500 to the government. To combat this, they invent the 'brilliant' notion of lying on their tax return and Dick reworks the sums so that the government owes them several hundred thousand dollars. Sally attempts to help by setting up a failed home hairdressing business, but when women start arriving for haircuts, Harry and Tommy 'camp up' and take to the 'salon' to help. Lying doesn't work, however, and the Solomons are faced with an audit - and the threat of being exposed as aliens.