Really, of all Batman's enemies, no two characters better personify the masks of comedy and tragedy. It's no wonder that they've been known to spar over the years, usually with the Joker somehow managing to make Harvey's life even worse. Really, I could do a whole post of the top five ways the Joker's screwed over Two-Face.
One of their earliest games of cat-and-dangling-bit-of-string occurred in the first issue of the Joker's own short-lived solo title:
I don't own this issue, so therefore I could not scan it for you guys. Thankfully, you can read the whole thing here, at the Grantbridge Streets and Other Misadventures, a great blog that regularly features wonderful comic and art scans.
There's not much to say about the story itself, other than it's pretty much just pure fun. I also appreciate that, while Two-Face is ultimately trumped by the Joker (as always), he actually makes for a formidable antagonist against Mr. J, to the point that their climactic battle could arguably be called a draw.
That said, my favorite scene of these two (hurr) facing (double hurr) off occurs earlier in the story: