Christopher Nolan confirms in Empire magazine that Harvey Dent / Two-Face is dead. Dead. Dead. Dead. As in: not alive, no longer living, dead.
Link to article quoting Empire on Two-Face, Joker, Catwoman and Riddler
Nolan said: "There are tricks that are fair and tricks that aren't fair. You DO see him dead. It was quite an expensive visual effect to stop his chest moving."