before i moved to canada, i filed single even though i was already married (this was advised by my US accountant).
When i moved to canada, i filed married, filing separately.
how it works is, when you're in canada you first file canadian taxes then use that information to get credit for us taxes.
if your husband is not a PR yet in canada or living in canada, then he shouldn't be mentioning your income or any canadian taxes on his us taxes because technically he isn't paying canadian taxes yet. i don't think he can get credit for the taxes you paid. he should only be putting his income information.
he does NOT want to mention you on his tax return AT ALL, even when he is a pr.
from what my us accountant told me, unless you are claiming a lot of deductions or making a lot of money, it's fine to file single even when married. he used his clients as an example... they have been married for 30 years, they file as single, and the IRS has never questioned it. some people advise against this. i didn't have any issues (knock on wood) with doing this. I switched to filing married, separately because i did my taxes in canada and i didn't want to have to fight about whether it's ok to do.
how did your husband file?