Mr. Quonset (Robert Morley) is the head of NAWA and is only interested in the organization's image with the public. Since the situation with Hoffman and Schmidlap threatens to become an embarrassment to NAWA, he just wants the next team sent to the moon to be a married couple rather than two males. Peter Mattemore (Jerry Lewis) is an astronaut who has been at NAWA for many years without having flown a mission. He is the only astronaut eligible for the mission, but unfortunately he is not married. He is, however, "practically engaged" to a waitress named Stella Mary.
Mr. Quonset informs him that he must be married within three days to a qualified astronaut. He tries to persuade fellow astronaut Eileen Forbes (Connie Stevens), who also has never been on a mission, to marry him, but she does not want to be rushed into marriage. She wants very much to be part of this one, but she is reluctant to go just as a means of fulfilling Mattemore's "masculine needs." Finally, Eileen agrees to marry Mattemore but insists that they be married in name only. At first Mattemore rejects the idea, stating that he would soon be crazier than Schmidlap, but after a few moments' reflection he realizes that he would rather go to the moon with Eileen under her prescribed conditions than with anyone else. The union is made official only forty-five seconds before launch.
When they arrive on the moon, they discover that there are two Russians living nearby at a Soviet lunar station. The Russians, Anna Soblova (Anita Ekberg) and Igor Baklenikov (Dick Shawn) are suspected of trying to sabotage the U.S. space station, but they are soon vindicated.
Anna then tricks Igor into marrying him by declaring she is pregnant. Once they are married she tells him the truth, and the Americans, who are now in love themselves, declare their intentions to have a "moon baby". As the film ends a race is on between the two couples to see who will be parents first.
The title song is performed by Gary Lewis & the Playboys led by Lewis' son, Gary.
Brian Keith has a cameo as General "Howling Bull" Hallenby.