Well, of course, there are those that ARE non-show tunes, Aretha Franklin's cover of Somewhere, for example.
Besides that, a good deal of MJL could pass for non-show tunes (I suppose some could be confused with non-theatrical art songs), though I'm not sure your friends would like those any better if they don't like theater music in general. Some pieces from Adam Guettel's Myths and Hymns, "Icarus" in particular, are a goood example of a little bit of both words.
Other musicals like Hair and Rent that are based on other styles would be good. Dreamgirls and The Wiz, if your friends like R&B, or the jazz influence in Chicago could make it a good pick.
"I could use a little...
Miracle."
~SWIWS