Married filing separate?

Over the past 4 years of our marriage, my husband and I have submitted our taxes as "married filing jointly". Each year our return has been smaller and smaller. This year we owe $364 if we file jointly. Whereas if we file separately I can expect a $2000 return and my husband a $800 return. Anyway, I asked our HR lady today why this keeps happening and she pointed out on my pay stub that I am claiming 1. I had no idea, but I suppose this must have been from our first year of marriage when my husband was not yet allowed to work in the US and I just never made the change. So essentially we've been losing a lot of money because of this and I'm miffed. So my question is, if we've filed jointly for the last few years, can we file separate? Is that an option? Or would it cause more problems further down the line.