Do I include my dependent's (father) 1095-A as a part my tax return?

Yes, include form 1095-A in your income tax return. Form 1095-A, Health Insurance Marketplace Statement, provides you with information about your health care coverage if you or someone in your family enrolled in coverage through the Health Insurance Marketplace.

• Use the information from Form 1095-A to complete Form 8962, Premium Tax Credit, and reconcile advance payments of the premium tax credit or – if you are eligible – to claim the premium tax credit on your tax return.

Since your father is your dependent and he has no income, he would not file an income tax return.

I have a follow-up question to this: what if the father in question is married and will file jointly (only to receive a refund)? Per IRS rules, I know he can still be claimed as a dependent in this case. But would form 1095-A be used on his tax filings or on the child's (who will claim him as a dependent)?

Why not just dropping the parent from the income tax return?
I'm on the current scenario of claiming a $500 deduction for a parent and having to pay $4,984 the Annual Tax Credit  because the parent has a 1095-A ( and not income)