A useful definition of counterpoint here with a brief explanation of the main types of counterpoint and a glossary of terms.

I think what we mostly get in folk music is counter-melody. That is, an independent melody which is part of an accompaniment to a song or tune and is in a subordinate role to the main melody.

This seems to be more or less what Dick was hinting at in his last post and, IMHO, fits the example he linked to in his original post.

TheSession discussion which Jack Campin linked to above was originally based on this article and raised some quite interesting points before it degenerated into a trading of insults.