1960 comedy Who Was That Lady?

Joi Lansing, Janet Leigh, and Barbara Nichols the 1960 comedy Who Was That Lady?

To get back into good graces with his wife, with whom he has had a misunderstanding, a young chemistry professor concocts a wild story that he is an undercover FBI agent. To help him with his story he enlists the aid of a friend who is a TV writer. The wife swallows the story–and later real FBI agents and enemy spies become involved in the scheme.