You have to claim a dependent for Head of Household.
Who is a qualifying person for Head of Household
https://ttlc.intuit.com/community/family/help/what-is-a-qualifying-person-for-head-of-household/00/2...
But one of you can probably claim child as a dependent. Away at school is counted as living with you. Even if no one claims them as a dependent the child has to check the box that says he CAN be claimed.
Who can I claim as a dependent?
https://ttlc.intuit.com/community/credits-and-deductions/help/who-can-i-claim-as-my-dependent/00/267...
