I don't really think that Heath's Joker is or isn't permawhite. The visual motif clearly suggests makeup, but the scripting of the character and Jonah's intentions for him indicate supernatural or daemonic overtones. In that respect, it is possible that the glimpses of flesh through the greasepaint were introduced to suggest a human entity beneath it all, where it was absent from the characterisation. That's sort of the opposite of the comics, where The Joker's other-wordly appearance is impregnable, but he can be intimidated or broken like all the rest of us.
It's quite a neat reversal, but I find myself preferring the comicbook version in this respect. I only hope that, after a savvy recast, the clownish guise can be revealed as irreversible, in a continuation of the "escalation" theme.