Oh, their relationship is certainly very complex and nuanced. Bats despises Joker but there’s a level of respect there and fascination too. And there’s probably a fair amount of guilt, since he’s the reason Joker took his chemical bath in the first place.

Ah, the infamously vague ending of The Killing Joke. Always left me scratching my head. Like, what’s going on in the 5th panel? Is he shaking Joker? He’s certainly grabbing him in some way and his facial expression seems to shift from laughter to…something else entirely.

The current theory seems to be that Batman just looses it completely and the laughing stops because he’s snapped and killed Joker. The rest is silence, as they say.

Here’s an article and video about it: http://sequart.org/magazine/29540/on-interpreting-the-killing-jokes-ending-and-authorial-intent/

Interesting idea, anyway. 😀