Act II is the confusing part of this movie, which made me what to write this analysis in the first place, so I could better understand what happens. You remember: Bruce Wayne decides to turn himself in, but before he can Harvey Dent claims that he is Batman, which ends in a plot to capture the Joker.
Act II opens with the Joker’s first act of terrorism: he kills the vigilante dressed like Batman and tells
Dent has another plan. The following interpretation was not explicitly stated in the script so the plot could build suspense and surprise, but I think it is implied. After Batman tells Dent to schedule the press conference, Dent hatches a plan to capture the Joker. Dent will admit to being Batman, which will cause him to be locked up. He will be the bait. Gordon, who Dent believes is dead, will go undercover to escort the bait across town to County jail, and be ready when the Joker strikes. This is exactly as it unfolded, and with the help of Batman, they capture the Joker.
For a moment, Batman is winning again. The Joker is gone. Dent can clean up the city. He can retire the bat suit and be with Rachel.
But the Joker has his own secret plan. He has the mob kidnap Dent and Rachel, and forces Batman to choose which one to save. Batman picks Dent and Rachael dies. Dent is burned, setting up the final act of the movie.
Both Batman and the Joker are changed in this Act. Batman accepts that he cannot give up, probably forever. The Joker realizes that having the Batman to fight is a more fulfilling life than ripping off the mob. He tells Batman, “you complete me” and vows never to kill him. Thus the eternal conflict between these two characters is established in Nolan’s Batman universe. It is a relationship that will continue to define Nollan's Wayne/Batman—even if we never see Nollan's Joker on film again.