As I read Miller’s The Dark Knight Returns, Clark Kent and Batman are not exactly friends. They are more like veterans of the same unit who maintain cordial relations. Kent is barely present at all in the first two books, but he definitely looms in the background. We know almost from the beginning that a collision between the two must be inevitable. Kent is the last active superhero. He takes orders directly from the President; and we all know how Batman responds to authorities who try to shut him down.
I’m referring to Superman as Clark Kent throughout this post because I don’t think the name “Superman” appears anywhere in this novel. There’s a suggestion in book three that the word has been censored from the media and just using it is an FCC violation. Miller depicts Superman as a role and Clark Kent at the real identity rather than the disguise. Even the soldiers who work directly with Kent during operations refer to him by his last name. That’s an interesting piece of characterization, because Batman/Bruce Wayne is drawn from the opposite angle. Once he goes back into action, it’s clear that Batman is the true identity, not Wayne.