Filing separately is almost always a bad idea, if you don't have to. You get significantly worse tax treatment, particularly if you're not particularly well off and are using the standard deduction and could qualify for various credits or deductions (these go away when your income is very high).
See this article for an example of the various things that will be worse when you file separately. Your spouse will also have to agree to file separately - if he files jointly and you also file separately, that won't work, after all. (Technically, you have to agree to file jointly, but practically speaking it's common for one spouse to file on behalf of both without meaningfully involving the other.)
As far as a green card application, it could have some impact, as filing taxes jointly is used as evidence of marital status. It isn't necessarily a deal breaker, but it could add more complication - you might have to work harder to prove you're married, particularly if you don't have a tax reason for filing separately (in particular, it will look very questionable if you filed separately and paid more taxes for doing so).
My advice: file jointly. Give your work a W-4 form filled out in such a way that the correct amount of tax is withheld so you don't get any refund (at least for your part of things). A tax refund is a bad thing, because it means you paid too much tax before. Correct that, and the tax refund won't impact you negatively even if he keeps all of it.
