I think most US companies provide work visas, which are non-transferable (i.e., they're only valid for that company). It's a lot more hassle for them to get
green cards, and there's the drawback that the employee can easily leave, so there's not really much incentive for them to do it.
If your boyfriend hates his job he could probably go for interviews and try to find another company that's willing to organise a new work visa for him. Or you could marry him.