Melody - foreground, in the sense of being the most obvious line that people hear and remember

Harmony - background and foundation AND/OR added colour around the melody

Counterpoint - means different things depending on which century you're in. But truly independent lines are rare. A lot of so-called counterpoint is really harmonic colour with pretensions to independence or - in polyphonic music - the same line chopped up, delayed and repeated so it plays against itself.  

It's very, very hard to think of music which is pure harmony with no sense of melody at all. In classical music you often get boilerplate writing at cadences where the melody disappears and you get your II-V-I without much else happening. But elsewhere there's usually a strong sense of a melodic line, even when the focus is moving between the voices.

Backing vocals, keyboards, bass and guitar - harmony, counterpoint or just part of the furniture?