Eh, that was the weird thing about JP, his personality varied wildly. When we first meet him he's a completely normal college student, and throughout his time as AzBats, he's steadily more and more homicidal and cult-y, but it's a completely adult psychosis - a totally competent, informed, deliberate rejection of society and its rules. He was fucked in the head, yes, but in the same way that, say, Scarecrow is. A normal man with abnormal values.
Then once he spun off as Azrael again and started getting costume changes and his own series, suddenly he was naive childlike raised-by-wolves boy who had a twelve-year-old's understanding of the opposite sex and no comprehension of the existence or purpose of perfume. Out of nowhere, he's a completely abnormal man with normal values... a male Cass, as it were.
But only half the time. The other half the time, he acted like a perfectly average American college student who'd suddenly gotten sucked into a bizarre world of superheroes and prophecy.
I mean, admittedly he did, explicitly, have a split personality, but that wasn't the split. The Jean-Paul half was supposed to behave consistently; the conflict was supposed to be between "normal good-natured guy" and "divine assassin," there really wasn't supposed to be anything fucked-up about "normal good-natured guy" beyond "periodically turns into divine assassin." Which is not a good match with Cass' fuckedupedness, which just makes her emotionally ten years younger than she physically is, all the time.