If you are married and live with your spouse, you can not file as head of household.

You can not claim a spouse as a dependent.
See page 11 of IRS Publication 501 which says:

“Your spouse is never considered your dependent.”

You can find IRS Pub 501 at this link:
https://www.irs.gov/pub/irs-pdf/p501.pdf

What you can do is file as Married Filing Jointly even if one of you has no income.