There is an option to file within D.C. as married filing separately but there are only a few situations in which this status can be used. This link lays out the exact scenarios in which you can file separately within D.C. under question #6. If you qualify for any of the scenarios presented to file separately, you would report only your spouse's income on the D.C. return, but you will need to split any income for any accounts that are registered in both of your names.
As far as Virginia, once your husband establishes his residency in Virginia, he would no longer need to pay taxes on his earnings to D.C. since Virginia and D.C. has state reciprocity agreements. This means that any income earned while working in D.C. but living in Virginia, would only be taxed in Virginia from the point residency is established. He may need to ask his employer to withhold state taxes within Virginia going forward if he hasn't already. Please see this link for additional information.
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