In other words Batman is literally an immortal god that can never age or die.
Last I checked the story details are that if Batman dies, he just gets reincarnated in a new fresh born baby body that looks just like a younger version of his original body with all his memories intact. He starts from the prehistoric times and continues reincarnating all the way to the present.
What more evidence do you need?
Sounds like you're getting confused with what Morrison had stated and also applying "Whatever Happened to The Caped Crusader" by Neil Gaiman to the state of Batman's being. That particular story was more of a nod to the history of Batman and has no bearing on continuity.