I think of counterpoint and harmony as separate things but they are really both happening all of the time. In fact, the only situation where you do not have harmony, you cannot have counterpoint, which is to have a monophonic instrument playing solo. Harmony can be implied in such a setting but it is not actually there. I would argue that parallel motion of multiple voices is not necessarily counterpoint, such as Gregorian Chant when adding a fifth, which could be constituted as harmony, so harmony can exist without counterpoint's presence, however rare that may be.
Its seems that people tend to think of harmony of in two ways. Some tend to think of it as any combination of notes heard simultaneously, while others tend to think of it as chords. The Harvard Dictionary of Music defines it as, "The relationship of tones considered as they sound simultaneously. and the way such relationships are organized in time; also any particular collection of pitches sounded simultaneously, termed a chord." So it is basically both but I would argue that a chord is harmony but harmony does not necessarily have to be a chord; it could be two notes sounding together or a tone cluster that cannot be defined as a chord with conventional theory.
Similarly, there seems to be a common misunderstanding about counterpoint. It is most often thought of as a system of composing, exemplified by such music as the Baroque era. While this is entirely true, it does not encompass the entirety. Just about any time you have two or more voices, you are engaging in counterpoint. So the broadest of definitions will tell you that almost all music you hear that is not a solo monophonic instrument is counterpoint. When I hear modern music from the rock and pop spectrum or jazz, I cannot help but think of it as contrapuntal in nature. Let's take jazz: walking bass line, melody, sometimes horn lines; these things all act independent of each other. When we study counterpoint, we are taught that counterpoint is the system of composing, instead of this literal definition, so it is often thought of that way.
My distinction here would be that of a literal take on it and a practical take. Literally speaking, nearly everything is counterpoint. In a practical sense, counterpoint is the composition approach. The reason why jazz would not necessarily fit the practical definition is that it does not follow the rules of classical counterpoint. The system of composing that we refer to as counterpoint focuses on how to have 2 or more voices acting independent of each other and the voice leading rules are specific to how we can make sure the different voices are perceived as independent. Parallel fifths are not allowed basically because the two notes are so closely related, due to the fifth's low position in the overtone series, that when you have parallel fifths, it sounds like a voice is suddenly missing from the texture. In the practical definition, harmony in counterpoint is secondary and results from the rules of classical counterpoint.
Again, with harmony, a similar distinction of literal/practical. Literally harmony is any combination of two or more notes. Practically harmony is a description of the combination of voices and is described as chords. Chord theory was developed somewhat during the Baroque era and solidified in the Classical era. So with my practical definitions, counterpoint was well underway long before harmony was in the picture.
To throw a wrench in things a little, we could also argue that due to the natural occurrence of overtones, harmony exists at all times with anything other than perhaps a pure sine wave. But that's just food for thought.
