How to handle eyeballs on a transparent character?

You can see through the whole character, but its eyes are solid. So what I want to do is make it so you can't see the eyeballs at all looking through the back of the character, only from the front, and only where they are not covered by the eyelids. If that doesn't make sense, I can post a picture- but basically, I'm trying to make the skin mesh obscure the eyes as if it were opaque but everything else you can see through it.

I don't know how to go about that; but I assume a second eye socket model with a custom shader is required... Maybe someone has already solved this problem for their game?