I am not really a fan of Billy Joel, but when I like one of his songs, I can be really quite obnoxious about it. So it is for this song. It appears on 1982's The Nylon Curtain.
According the various Billy Joel sources on The Information Superhighway, the song was never really released as a single, despite the hilarious and elaborate video that was made for the tune.
Here's a bit of trivia for you: before Joel married Christie Brinkley in 1985, he had romantic entitlements with two other models: Elle MacPherson and Whitney Houston (who had quite a promising career as a model until she, you know, opened her mouth to sing and Holy Heaven came out.)