Bob...I've never encountered this situation, and my initial reaction was no.  With that said, I did research and found this article.  That's why I'm seeking input.  

https://turbotax.intuit.com/tax-tips/family/guide-to-filing-taxes-as-head-of-household/L4Nx6DYu9

Can two people file Head of Household on their return?

Two people cannot file as Head of Household on the same return. If they are married, then they typically have to either file as Married Filing Jointly on the same return or as Married Filing Separately on separate returns.

Two people can both claim Head of Household filing status while living in the same home. However, both need to meet the criteria necessary to be eligible for Head of Household status:

• You both are unmarried.
• You both are able to claim your own qualifying dependent.
• That dependent resides at the same residence for more than half the year. (In the case of a parent, they can live elsewhere. However, you still have to provide them with at least half of their support.)
• They both have to pay more than half of the cost of keeping up the portion of the home for themselves and their dependent(s).