Oh, Batman absolutely has some sort of mental disorder. The Joker's joke at the end of The Killing Joke (How many times can I use the word 'joke' in one sentence?) illustrates this rather nicely.

"See, there were these two guys in a lunatic asylum… and one night, one night they decide they don’t like living in an asylum any more. They decide they’re going to escape! So, like, they get up onto the roof, and there, just across this narrow gap, they see the rooftops of the town, stretching away in the moon light… stretching away to freedom. Now, the first guy, he jumps right across with no problem. But his friend, his friend didn’t dare make the leap. Y’see… Y’see, he’s afraid of falling. So then, the first guy has an idea… He says 'Hey! I have my flashlight with me! I’ll shine it across the gap between the buildings. You can walk along the beam and join me!' B-but the second guy just shakes his head. He suh-says… He says 'Wh-what do you think I am? Crazy? You’d turn it off when I was half way across!'".

The joke is a sort of allegory to their lives. The bridge of light is a metaphor for redemption, goodness, justice, the ability to change the world with his 'light'. The character in this joke which represents the Joker doesn't turn down this offer because he doesn't think it's possible, but because he can't believe Bruce would really help him. The difference between the two isn't that one believes in good and the other doesn't, but that Batman believes in humanity and Joker doesn't. But one key aspect of this allegory that often goes unmentioned is that fact that they're BOTH insane for believing the bridge of light would work in the first place. Joker's insanity is obvious, but Batman's is a bit more subtle. Batman lives in a state of constant denial. He denies that the world is beyond fixing, that some people can't be redeemed, and most importantly, that he's just a man, and that his plan to save the world by beating up lowlifes and putting them back into the same prisons and asylums they keep walking out of is in itself crazy. He can't accept reality, because reality destroyed him. In more ways than most people realize. A dialogue from Batman Beyond tells the story better than I could. Prior to this, a villain who manipulated sound, and posed as a voice in Bruce's head, trying to convince him to kill himself.

Terry: Tell me something - why were you so sure those voices weren't coming from you?

Bruce: Well, first, I know I'm not psychotic.

Terry: I hope your other reason is more convincing.

Bruce: Second, the voice kept calling me "Bruce." In my mind, that's not what I call myself.

Terry: What do you call yourself? [Bruce just looks at him for a moment] Oh, yeah. I suppose you would. [Batman voice] But that's my name now.

Bruce: Tell that to my subconscious.

In all the ways that matter, Bruce Wayne died alongside his parents in the alley. He can't even accept that he is Bruce Wayne anymore, and considers that name a disguise for the new persona he created to replace him. It's not just that he considers his role as Batman more important than his role as a wealthy businessman, but that he considers Batman to be his true identity, and Bruce Wayne to be the mask he wears to protect it.