I’m in the same class as him.

Alright, this phrase sounds wrong to me. I feel like the correct phrase is “I’m in the same class as he is.” However, when I turn it around and say “He’s in the same class as me,” it sounds correct. If I were to use the same structure as “as he is,” the correct phrase would be “He’s in the same class as I am.” This also sounds correct, but I almost never hear it.

To most native speakers of any language, grammar and sentence structure comes naturally to them, and they can tell whether something is right or wrong by how they “sound” or how they “feel.” This is true for me, but for some reason, I can’t figure this one out.