The Americans and the Russians each have a two-person base on the moon. The Americans have had to keep replacing their astronaut teams because they quickly go crazy; they have been using only male astronauts on the unspoken assumption that this would avoid any possibility of impropriety. The Russians, as godless Communists, are under no such constraints, and their male-female team has remained well-adjusted. At the start of the film, a male and female American astronaut team is sent up to replace the sex-starved all-male team. The government insists on them being married first to preserve morality. Most of the story revolves around the eventual consummation of this marriage of convenience, and around their relationship with their Russian neighbors, who keep casually dropping by.

Jerry Lewis is Kreton, a childish alien who, against his teacher's will leaves his planet to visit the Earth, and lands in the backyard of a famous television journalist who doesn't believe in U.F.O's and aliens. Wanting to study humans but not able to fully understand them, Kreton makes a mess out of it, generating a lot of comic situations.

Sidney Pythias (Jerry Lewis) is the a bumbling janitor picked up by cop Darren McGavin as a teenage gang member worth saving from delinquency. With McGavin's help, Sidney works his way through the Police Academy to become a cop too.

Barbara is a very rich girl who falls in love with Norman Phiffier, a poor young man. She doesn't tell him who she really is and prepares to marry him. But, Mrs. Tuttle (Barbara's mother) doesn't want her daughter to mary such a poor man. So, she hires Norman at one of her big stores, and gives him the most difficult and disgusting works. She hopes that seeing Norman humiliated, Barbara will finally leave him. But things don't work exactly this way...

The arch-villains of the United Underworld - the Joker, the Penguin, the Riddler and the Catwoman - combine forces to dispose of Batman and Robin as they launch their fantastic plot to control the entire world. From his submarine, Penguin and his cohorts hijack a yacht containing a dehydrator, which can extract all moisture from humans and reduce them to particles of dust. The evildoers turn the nine Security Council members in the United World Building into nine vials of multicolored crystals! Batman and Robin track the villains in their Batboat and use Batcharge missiles to force the submarine to surface.