Batman sired a child with Talia al Ghul during their marriage, named Ibn al Xu'ffasch. Dennis O'Neil mentioned that this story was ignored from continuity around Zero Hour because it did not fit in well with the rest of the mythos. Infinite Crisis brings most of this back into continuity with the story Batman and Son by introducing Damian Wayne and stating that Batman was drugged and pretty much raped.
In the world of DC, there were really two Batmen if you think about it. One as "the world's greatest detective" who typically fought other non-powered street-level characters like the Joker. The other was a man who defied all odds as a human, and went toe-to-toe with super-powered villains and cosmic threats alongside the Justice League. Loeb and Lee balanced this duality into one series and did the same with the Batsuit as well. It's almost a combination of the classic blue and gray suit we know best from the Adam West series, mixed with a little bit of Frank Miller's Dark Knight Returns suit. The result is a colorful suit that looks at home in the dark alley's of Gotham.
Meanwhile, Batman's relationship with the Gotham City Police Department changed for the worse with the events of "Batman: Officer Down" and "Batman: War Games/War Crimes"; Batman's long-time law enforcement allies Commissioner Gordon and Harvey Bullock are forced out of the police department in "Officer Down", while "War Games" and "War Crimes" saw Batman become a wanted fugitive after a contingency plan of his to neutralize Gotham City's criminal underworld is accidentally triggered, resulting in a massive gang war that ends with the sadistic Black Mask the undisputed ruler of the city's criminal gangs. Lex Luthor arranges for the murder of Batman's on-again, off-again love interest Vesper (introduced in the mid-1990s) during the "Bruce Wayne: Murderer?" and "Bruce Wayne: Fugitive" story arcs. Though Batman is able to clear his name, he loses another ally in the form of his new bodyguard Sasha, who is recruited into the organization known as "Checkmate" while stuck in prison due to her refusal to turn state's evidence against her employer. While he was unable to prove that Luthor was behind the murder of Vesper, Batman does get his revenge with help from Talia al Ghul in Superman/Batman #1–6.