Who pays for her health insurance does not determine if she can be claimed as a dependent.
If she meets all the requirements under the Qualifying Relative rules then you can claim her as a dependent on your tax return.
To be a Qualifying Relative -
1. The person cannot be your qualifying child or the qualifying child of any other taxpayer. A child is not the qualifying child of any other taxpayer if the child's parent (or any other person for whom the child is defined as a qualifying child) is not required to file an income tax return or files an income tax return only to get a refund on income tax withheld.
2. The person either (a) must be related to you or (b) must live with you all year as a member of your household.
3. The person's gross income for the year must be less than $4,200 (social security does not count) in 2019
4. You must provide more than half of the person's total support for the year.
5. The person must be a U.S. citizen or a U.S., Canada, or Mexico resident for some part of the year.
6. The person must not file a joint return with their spouse.
Since the issue is "do you pay more than half the person's total support", you would have to evaluate the cost of insurance as being a support cost paid by the parents, along with any other support provided by the parents; then evaluate any other sources of support (state benefits, welfare, section 8, etc); and the support provided by you; and add up whether you provide more than half.
An adult partner is never a qualifying person for head of household status, even if they are a dependent. You would need to be claiming at least one other dependent who is a qualifying person for HOH, usually your biological or adopted child.