If the original poster's example is Somethin' Stupid, then (from memory) Frank's pitch never goes above Nancy's: his voice carries the melody, and hers is a descant less than an octave above it. Drop her voice by an octave, and it becomes a more usual harmonising.

I can't honestly think of a better expression for it than "the bass carries the melody", though perhaps "inverted harmony" might be appropriate; it's certainly effective (er, "somethin' different"?). For comparison, I used to get thrown by hearing Paul Robeson sing on the wireless in the 1950s, as the piano accompaniment was pitched above his voice --- this seemed Just Wrong to my six-year-old ears, but I later realised the piano couldn't do anything else to accompany a bass-baritone.

Hope this helps, and apologies for the blethers. Now, if you'll excuse me, I've got an earworm to evict .... :-(