Actually, Joker loves the Batman. In a very twisted way, of course. He seems to live for nothing more than his confrontations with the Batman (and consequently, durring No Man's Land, got extremely depressed when Batman started ignoring him; his first words, when Batman finally appears to foil his crimes, are "What kept you?"
It's familiarity.
You get it all the time.
Professor X/Magneto, Batman/The Joker, Optimus Prime/Megatron, Spider-Man/Venom, Thanos/Everyone.
Some people become so used to the challenge of having someone compete with them that when they are gone or when they actually think about it, they realise it wouldn't be as satisfying to go about their evil ways without their opposite pole if you were.
Prof X and Magneto always admired each other and respected each other. That Batman/The Joker thing. Optimus Prime and Megatron from Transformers had respect deep down. Venom views Spider-Man as a worthy for or at the very LEAST respects him next to Carnage who just doesn't give a damn and we all know what happened to Thanos when he wiped out everything in "The End."
-AC