Yes, he battles the Inhumans, but only the evil ones.
Well, most of them are evil. The others? Wrong place, wrong time.
In pages of The Incredible Hulk Special released in 1968, the Hulk is inadvertently drawn into an Inhumans' coup thanks to Lockjaw -- who teleported Hulk to a prison dimension because Hulk was being, y'know, Hulk.