As a New Mexico resident, your husband is otherwise taxed on all of his income, worldwide, no matter what the source, by the state of New Mexico.  It is also a fact that income earned in Washington is considered "Washington-source" income; and so that would normally require paying income taxes to Washington, regardless of his residency -- but for the fact that Washington has no personal income tax system.  (However, if your husband is self-employed, then he may have to pay Washington state B&O or sales taxes, which is another matter.)

For income tax purposes, though, your husband would not be considered a Washington state resident for any part of the year, and would instead be a full-year New Mexico resident for tax purposes.  For any income earned or other economic activity undertaken in Washington state, he would be considered a nonresident.

Thus, in TurboTax, you will simply enter that you (and your husband as well) are residents of New Mexico.  Because Washington has no personal income taxes, you won't need to make any other entry, anywhere in the program, related to your husband living in Washington.

In other words, for income tax purposes, his absence from New Mexico is considered "temporary" and does not change his residency status . . . even if he physically spent more calendar days during the tax year in Washington than in New Mexico.

Thank you for asking this important question.