Yes, absolutely! If you are on an HSA-qualifying HDHP which covers your spouse and/or family members, then you can contribute a higher amount than if it were just you on the plan. If however, those people can be claimed on another person’s tax return, then you would be unable to contribute the higher amount. The family max is $7,000 (2019) and $7,100 (2020) and the individual max is $3,500 (2019) and $3,550 (2020).
Regardless of your eligibility and how much you can contribute, you can use your funds to pay for qualified medical expenses of dependents and family members. 1
1:IRS Notice 2004-50 Q&A 36