My husband lives and works in CA during the week (all year) while I reside in AZ in the house we own. We have one income. How should we plan to file our taxes for 2020?

[jtorres614]

One income household with dependents.

[KittyM2]

Is your husband an established Arizona Resident who took a job in California, or a California resident attempting to establish Arizona residency?

[jtorres614]

Currently CA resident wanting to continue his residency while I reside in AZ.

[KittyM2]

In this case, you will file a [Joint] California Resident return. You may or may not need to file an Arizona Non-Resident return.

[TomD8]

You must file in both states.  That's because both AZ and CA are both community property states.  Here is AZ's rule on your situation:

If your nonresident spouse is a resident of a community property state, then the total community income will include income from both Arizona and the state where your spouse is a resident. Total community income would include wages you and your spouse (if a resident of a community property state) earn while you are married.  

https://azdor.gov/sites/default/files/media/PUBLICATION_200.pdf

As an AZ resident, ALL your income is taxable by AZ.  Since you have community income from your husband's job in CA, you must file an AZ tax return.