I have two dependents that I qualify to claim on my taxes. I fully support these dependents. However, we live with family. Can I clam Head of Household?

Probably not, based on on your statement that you live with relatives and and do not pay rent.  One of the Head of Household filing requirements is that you pay for more than half of the cost of maintaining a qualifying household. This portion must be for the entire tax year. Qualifying payments include more than half of the total household bills. These bills include rent or mortgage, utility bills, and insurance. They also include property taxes, groceries, repairs and other common household expenses.  For more information on claiming Head of Household, see the following TurboTax Online Publication:  Guide to Filing Taxes as Head of Household.