The Turner Classic Movies (TCM) cable channel ran the 1942 film "This Gun For Hire" last night. TCM's host for the film was Eddie Muller, a writer specializing in "Film Noir" topics, who described the two stars of the film, Alan Ladd and Veronica Lake, as "they are like male and female sides of the same coin". One example could be this one where one side was designed by a man and one side designed by a woman: United States Commemorative Half Dollar 1938-S Oregon Trail Memorial Laura Gardin Fraser designed the Indian and James Earle Fraser designed the covered wagon. Let's see if we can find coins with a male and female side.
Any coin with Elizabeth II has an instant "female side." That leaves a wide swath to choose from. The same could go for any coins with Liberty. But I'm not sure if that's what you have in mind.