Spider-Man/Batman is about as good as most inter-company superhero crossovers get (as in, it's perfectly fine, but only just a step above fan fiction, despite the dream team of JM DeMatteis and Mark Bagley), and doesn't even bother to explain how the two fictional universes have gotten mixed up. It's just all of a sudden, Marvel's New York and DC's Gotham City exist in the same world, and both The Joker and psychotic symbiote Carnage are both guinea pigs in an experimental treatment where they have chips stuck in their heads to stop them being so crazy.
Which obviously doesn't work, because then there wouldn't be any reason for the two superheroes to team up and defeat their mortal enemies. Carnage deals with his chip pretty easily and then springs The Joker from his prison as well, with the two of them heading on a psychotic crime spree with their shared understanding that the world is chaotic and life is pointless. Then they start arguing, giving Spidey and Bats a chance to stop them.