Listen, maybe Harvey Dent was just really groggy or something
Groggy and delirious, a bedridden Harvey Dent shifts around uncomfortably and tries to take in his surroundings. Leaning down to greet him from his drug induced slumber is a nurse whose face we can’t see. That seems nice and all, except—surprise! The nurse turns out to be the Joker.
The true identity of the nurse isn’t immediately processed by Harvey, who can’t put two and two together while in his medicated stupor. Blackened eyes, face full of white clown make up—nah, just a normal person. Maybe it was just that surgical mask? In true comic book fashion, obscuring any part of one’s face will immediately conceal the identity of the wearer, leaving everyone else none the wiser.
And while, sure, there are probably a lot of scenes that you could splice down to five seconds to make seem more absurd, Harvey pushes our suspension of disbelief pretty far. As Two-Face himself would certainly pledge, there are multiple sides to every issue, this one included.