The first Drow to enter the cavern was seen to cast the spell, but additional drow will probably cast additional darkness spells in order to expand the effected area and maintain the darkness. Daylight is the counter spell, and Dispel Magic should also work. Now here's my question: Considering that the Drow who cast the spell are themselves blinded, would they know when their Darkness is dispelled? I think they might, since they have the ability to de-activate the spell at will, and I assume this means they can "feel" the spell's presence. Also they might hear a counter spell being cast, assuming they could recognize it.
There are 11 Drow attacking, in a sort of "Forlorn Hope". Since they are blind, it is unlikely that they will use their crossbows. Nippy has already engaged one. Since they also have to fight hand-to-hand, they probably won’t be levitating either.
I'm sorry for bringing in all this darkness stuff, but I just finished playing HotU, where the Drow successfully cast darkness on my epic level half-elven Cleric/Champion of Torm (named T'lainya!
One interesting aspect of both HotU and War of the Spider Queen, is the disappearance of Lolth, causing her clerics and all the Matron Mothers much consternation. This actually fits rather well with out story, in that it gives the Drow a reason to be helping out with constructing the Abomination, since they think that Lolth had taken over Moander's avatar. It also means that Drow clerics who worship Lolth have to rely on scrolls and artifacts for their power. I find that very interesting.