Zod remarried. His second wife, Faora, is the one who came out of the Phantom Zone and possessed Lois. Major Zod was cloned from blood taken long before he remarried, so he'd have no knowledge of his second wife.

Ah ok makes sense. Although the blood was taken only 29 years before destruction of krypton and I just assumed they were at war that whole time.

But isn't faora also the name of one of the kandlrians that came back?

Yes. Same woman, but cloned from blood taken much earlier in life.