As readers, we unconsciously forget that it is essentially the same person talking throughout. That's a credit to the craft, I suppose. Still, it's funny to be writing a conversation between two mentally unnerved characters...they're mentally unnerved? I'm the one having a conversation with myself.
The most amazing example of this for me is Umberto Eco's The Island of the Day Before. The entire massive book is a philosophical discussion between two characters. The fact the he was able to argue both points of view so thoroughly and convincingly is astounding. At least with mine, I have the luxury of having two characters who agree.