It's not actually a zombie apocalypse story. The Earth's covered in billions of zombies, yes, but they're not the main threat. Our heroes will find a cure. They'll even argue about zombie-killing, because these unlives could have been saved. Instead, the problems include:
(a) zero-empathy rich supervillains in Australia who think they're saving the world. Ironically, though, if it hadn't been for the cure, they would have been.
(b) If the dead are loitering on Earth, they're not on the fires of torment for all eternity. The infernal legions don't like this. A big guy with horns is coming from Hell to sort that out.
(c) okay, yes, the undead are dangerous too.
It's a major showcase for DC's odd, weird and mystical characters. Swamp Thing, Zatanna, Dr Fate, Deadman, the Phantom Stranger and the Spectre appear, but the most important is John Constantine. Naturally. As is right and proper. If Hell's involved, you want the Hellblazer. He's a complete and utter bastard and he has a plan. The story's built around him as much as around the regular superheroes and he's about to live up to that punchline he gave us in DCeased: A Good Day to Die. I love Constantine and I'm pretty sure Taylor does too.
It's a strong story for the heroes too, though. Superman is all-important, while Taylor makes me love the Bat-family I'd been wanting dead when I was reading their own Bat-books. I love the whole bunch, except for a certain ex-Robin who (hurrah) dies.
There's a triumphantly happy ending... ish. They've cured all the zombies, including some resurrections we'd never expected, but the narrative's so single-mindedly happy about this that it perversely pushed my attention towards the darkness. Two billion people have been saved? That's impressive, but it still leaves nearly six billion dead, including a lot of people we know. Our heroes can only cure infection, not actual death. There are also dangling plot threads: (a) undead Darkseid on the rampage, (b) undead SPOILER eating the sun and making the Earth colder. Those are not minor details.
I've still thoroughly enjoyed DCeased, though. It improves when you read all of it. Definitely recommended, even to people who aren't really into zombies.