@jburatti we need some more details about the situation as not enough information was provided.
in order to file HOH and you are still legally married, you must
1) have lived apart for the last 6 months of the year or be LEGALLY* separated as of 12/31
2) you and your spouse are filing separate returns
3) you provide more than 50% of the household expenses
4) your home is the main home for your bio, step- or foster child and the child must have lived with you for at least 6 months of the year. (no other relatives will meet this condition - it is specific to your children).
5) you claim the child as a dependent.
you must meet ALL FIVE conditions. you asked if both can file HOH - depends on the circumstances. It is also possible that neither of you can file HOH.
The typical case (but may not be yours' as more information is required) is the children live with Mom while the Dad lives alone. Mom can meet the 5 requirements and files HOH; Dad does not and files MFS. (dad can not file SINGLE as he is still married).
Also, you spouse did not file HOH and MFS - it was one or the other.
does that help?
* in some states (e.g. NC), you can be separated, but not LEGALLY separated. Legal separation requires a court order; not just two people who say they are "legally separated"
