Because your husband is in the military, he can keep his state residency in California, or switch it to Washington. You will qualify for the same as a military spouse. So either of you, or both, can claim a resident state in California or Washington. You can keep your California license if you decide to remain a California resident.
In addition, your income is reported in the state you are physically when you did the work, not where the company is located. So you would report it in Washington, except there is no individual Washington income tax, so you will not need to do so. You company will not need to pull state withholding for those wages earned in Washington.
Click here for more IRS information about taxes in the military. There are exceptions for those in service.
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