No. Since your husband is not a Virginia resident, he doesn't need to file a return there. While you are a VA resident, you also don't need to file a return if you had no income.
When one spouse is not a resident of VA, the spouse who is prepares a "mock" separate return with only their own income and deductions. Since your separate income is below $11,950, you would not be required to file. There would be no reason to file either.