I was thinking of Frank Loesser's "Baby It's Cold Outside," too - it has the same "gfeel," but I don't think it has two people singing different melodies on top of each other. It's more of a question-and-answer song, or something like that. It made me look up Loesser in Reading Lyrics and I think I found one that fits the bill, although maybe it's more of a "fugue": "I Believe in You."

Here are the lyrics:

You have the cool clear eyes of a seeker of wisdom and truth,
Yet there's that upturned chin and the grin of impetuous youth,

I believe in you, I believe in you.

I hear the sound of good solid judgment whenever you talk,
Yet there's that bold, brave, spring of the tiger that quickens your walk,

I believe in you, I believe in you.

And when my faith in my fellow man all but falls apart,
I've but to feel your hand grasping mine, and I take heart,
I take heart to see the cool clear eyes of a seeker of wisdom and truth,
Yet there's that slam, bang, tang, reminiscent of gin and Vermouth,

Now I believe in you, I believe in you.

(musical interlude)

I believe in you, I believe in you, I believe, I believe in you.