Sort of half-and-half, really. I mean, he doesn't use light-hearted fare, but he certainly uses a humorously cruel tone, utilising sarcasm, irony, dramatic irony and especially mockery, for instance:
* Tricking his gang into killing each other, ending in a bus crashing through the wall at the exact moment he says he was gonna kill the busdriver * Tricking the bank manager into thinking he was about to die when he was really just using a simple gas bomb * The extremely sarcastic 'pencil trick' * The 'drop her? Poor choice of words' * The supposed origin stories delivered as if telling a long joke * Mocking of authority figures and authority itself - sarcastic jabs at the gang leaders ("You should like my suit. You bought it"), sarcastic criticism of Batman's interrogation technique, morals and personal philosophy, sarcastic applause as Gordon is made Comissioner * Use of irony in his speeches - e.g., the final speech mentioning gravity as he hangs upside-down on a rope * Near 4th-wall levels of jokes only the audience could appreciate - e.g., the walking away from an exploding hospital scene
Basically, the portrayal ramps up that aspect of the character that realises that life and aspects of order are very cruel and must thus be mocked with anarchic and ironic violence.