Wrong!
You probably got confused in people. First of all, it would have been John Leguizamo as the Joker. Remember he was the Clown in the Spawn Movie. He was fantastic! And Britany Murphy from Sin City is a Harley Quinn in the flesh and blood. The blond hair, the figure, and she had the smile for it.
Correction corrected corrected
I meant to say "clown-colored flesh".
All of that notwithstanding, these newer films take a much more modern, "realistic" approach. I can see how they might have all of the Joker's appearance be artificial, and still preserve his essential character, that of a man who has been driven mad by a moment of tragedy; thus casting him in the role of The Batman's mirror image, one who suffered tragedy and became a monster in service of evil, rather than The Batman, who became, arguably, a monster in service of good.
Correction corrected
The entire clown appearance of the Joker is permanent. In the scene you refer to in the Tim Burton version, the makeup is flesh colored; Joe Chill (Joker) is wiping off the flesh colored makeup to reveal clown colored makeup. Now, that assumes you consider the Tim Burton versions authentic; in my opinion, they belong more with the Adam West comic versions, and less with the Bob Kane/Frank Miller vision of The Batman as a tortured anithero (despite Kane's cameo in Burton's 1st film). Either opinion is valid, I just prefer the more traditional "dark" intepretation.
That said, more foundation for the idea that the clown appearance is "permnanent", is the origin sequence of the Joker in Brian Bolland/Alan Moore's "The Killing Joke", a short graphic novel that may be the only explicit telling of The Joker's origin in comic book form. That book clearly shows the clown appearance as a byproduct of the Ajax Chemical accident. Kane himself does not explain the maniac's origin.
You're Corrected
The only thing that was "permanent" on the joker was the shape of his mouth, and his hair of course. Everything else is makeup.
If you watch Batman with Micheal Keaton there is a scene with The Joker and Michelle Phifer's character in that museum and she throws a glass of wine on his face. He jokes about melting but then reveals his face and the make-up is smearing away/.
