Well, he maintains control over his faculties on the whole, & living a double life does not equate to multiple personality disorder, & it would be a pretty big stretch to call him paranoid or delusional, because what he deals in is real. So by all rights, he is a sane individual
Does he suffer psychoses, or emotional disorders, perhaps even PTSD? Most assuredly so. In fact, he should get together with Frank Castle (The Punisher) and start a support group
Psychoses? No way. As I discussed above, psychosis means loss of touch with reality, and you just said that he's entirely in touch with reality and in control of his faculties. So by using that word, you're contradicting yourself. Behavioral or emotional disorders, possibly, but not psychosis.
And Batman would be too busy trying to put the Punisher in jail to want to go into therapy with him. Maybe some of the gross misinterpretations of Batman, like the Tim Burton version or the Frank Miller G*ddamn Batman, could be likened to Castle, but the real Batman is dedicated above all to fighting those who deal death casually and without remorse, like the man who killed his parents so randomly. The Punisher represents everything Batman despises and has sworn to fight against. Sure, the Punisher has a tragic past motivating his crimes, but so do Two-Face and Mr. Freeze and a number of Batman's other archenemies.