(I am *not* a tax expert, but I thought I'd share my own experience. It's only my experience, though.)
I am USC married to a UKC. We live in the UK. I will be filing as "married - filing separately" and I will be claiming my spouse as a dependent. He had UK income in 2012; he did not have US income in 2012. This is on the advice of my trusted tax advisor.
In order for me to claim him as a dependent for 2012, my spouse will need to have an Individual Taxpayer Identification Number (ITIN) -- this is a tax ID number for someone who isn't eligible for a SSN. We will have to fill out form W-7 to get the ITIN and submit W-7 with my federal return.