I just saw this duet done on some (Australian) TV show last week. The couple weren't great singers, but they were old enough that no one seemed to mind.

Joe asked whether there's anything like this in trad music. It has been mentioned in other threads that the two songs I Was Born About Ten Thousand Years Ago and Great Historical Bum are sometimes sung together, taking verses from each alternately. The Chad Mitchell Trio did that, and I think they finished off the performance by singing the two songs against each other. I recall there's some debate about how trad the two songs are.