Felix Farmer (Richard Mulligan) is a Hollywood director well on his way to killing his career. He just spent $30 million making a musical that no one wants to see. But, after several botched suicide attempts, the filmmaker has a sudden epiphany: Why not turn his moribund family-friendly entertainment into a porn movie? Of course, to make his scheme work, Felix will have to convince his actress wife, Sally Miles (Julie Andrews), to bare it all for the camera.

Victoria Grant (Julie Andrews), a down-and-out British soprano, struggles to find work in the nightclubs of 1930s Paris. While trying to scam a free meal, Grant meets cabaret performer Toddy (Robert Preston), who comes up with an idea that will change everything. Acting as her manager, Toddy bills Grant as a male female impersonator. When the nightclubs eat it up, the duo makes it big – even a Chicago mobster (James Garner) is enamored with Grant. But keeping the truth a secret is no easy task.

During the 1820s, a domineering young minister, Abner Hale (Max von Sydow), and his compassionate wife, Jerusha (Julie Andrews), embark on a dangerous sea voyage to Hawaii. When they arrive, Jerusha befriends the Hawaiian people and embraces their customs and culture, while Abner, intent on converting them to Christianity, views them as pagan savages. Jerusha grows unhappy with her marriage and begins to fall for Rafer Hoxworth (Richard Harris), a past lover.

Professor Michael Armstrong is heading to Stockholm to attend a physics conference accompanied by his assistant-fiancée Sarah Sherman. Once arrived however, Michael informs her that he may be staying for awhile and she should return home. She follows him and realizes he's actually heading to East Germany, behind the Iron Curtain. She follows him there and is shocked when he announces that he's defecting to the East after the US government canceled his research project. In fact, Michael is there to obtain information from a renowned East German scientist. Once the information is obtained, he and Sarah now have to make their way back to the West.