Two part harmony is not counterpoint in the normally accepted usage, or not necessarily so.Things have got to go against each to make it counterpoint. Parallel thirds is harmony, but it assuredly isn't counterpoint. Pity you can't include music examples in the text on Mudcat, but try this. Sing Frere Jacques mentally(or with someone else), as a round in the usual way.
Now, when you get to the second line, one person will be singing Frere Jacques and the other witll be singing Dormez vous. These harmonise perfectly, but it's not counterpoint. But when you get to the next line, voice 1 is singing Sonnez les matines while voice 2 is doing Dormez Vous. Now, that is counterpoint: one voice coming down, the other one going up in a completely different rhythm.