There is no term that specifically denotes multiple simultaneous vocal lines while excluding multiple simultaneous instrumental lines. There are many terms that denote various ways in which multiple parts are played or sung at once, and some of those ways are historically or primarily vocal styles (fauxbourdon, for example).
Some of these terms (including some where there is relatively little independence among the voices) are:
And to counter your assumption that "counterpoint" cannot describe a situation with two independent melodies, consider the page Counterpoint Duet, which describes
A Musical trope. One character sings a song, then another character sings to the same chords but a different melody, then both sing together in counterpoint. Most often used to express arguments or show that characters have differing opinions on the same subject, though occasionally merely employed for fun.
Note the use of counterpoint to describe both characters singing together.
I don't suppose that a term specifically denoting vocal counterpoint would be very useful, because it is relatively efficient to add the adjective "vocal" to any of the existing terms. On the other hand, a term denoting counterpoint of independent melodies might be useful, because describing the concept requires a phrase of at least several words.
The 11th edition of the Encyclopædia Britannica (1911) has an interesting sentence on the topic:
The individual audibility of the melodies is a matter of which current criticism enormously overrates the importance.
The author of that article was Donald Francis Tovey.