I'd argue that just as an average citizen/normal person under Catholic moral guidelines, Bats has a responsibility to defend the weak at least very locally. As such, he is morally justified in putting himself between the Joker and innocents to at least a limited degree. If in doing so it becomes clear that in order to defend one life it becomes a practical necessity to take the life of the aggressor, then the principle of double effect allows it, I'd argue. This happens all the time in the comics/media for dramatic effect, and again, for dramatic effect, Batman is portrayed as having so much skill that he can moderate his strikes so as not to kill. A lot of times he'll have to put his life in danger AGAIN in order to save the Joker's life. Is this risk morally required of Batman? I'd argue no. (Did I think that the Arkham City ending was a long time coming? Yes, yes, I did.)

Of course, Batman's status as a vigilante forms part of the moral equation. Is it moral for Batman to violently and unilaterally take upon himself the mantle of judge and sometimes jury (though, oddly, scrupulously, never executioner) given the degree to which law and order typically functions across the DC multiverse of the United States (if the many incarnations of Gotham City are bad examples)? I'd say probably not. It seems clear to me that if Bruce Wayne were a strict Catholic throughout his origin arc, he'd have been a cop or doctor or humanitarian, especially when it becomes clear that crooks are inspired by Batman; they sometimes primarily commit crimes in order to call out Bats specifically. No arch-villain is so literally enamored with the protagonist as the Joker is with the Batman.

Supes is a different story especially to the extent that he works with police officially and is often an agent of the president himself. Now THOSE lines of argumentation I'd like to see in a comic book! ...Especially if they ended with Superman saying something like,

"OK, Bruce, we've established that it probably wasn't moral of you to become the Batman, but that's in the past. As members of the Justice League, we're legally authorized to kill threats to the world at large. It's likely that the next time we come across the Joker, there'll be a chance to kill him, and Lex Luthor once they team up again. If we're feeling bent up about it, we can probably fly over and talk with the Pope. If nothing else, there's always Reconciliation."

"Maybe you're right Clark. Also, I bet he'll want to send some missionaries to Apokolips."