An HSA is not a product you buy. It's a savings account run by individuals (not couples). All you need to be able to open an account is cover from an HDHP meeting the current rules. The plan does not have to be in your name so long as you have cover, say, as a spouse. Note you can have other policies to pay some of your health costs for disability, long-term care and specific diseases. But you are ineligible if you have already signed up to Medicare or, as a member of the armed forces, you have Tricare. It's up to you to check what you are allowed to have. Your employer can set up a savings plan (although you cannot have both an HSA and a general HRA at the same time) or you can go to a bank, credit union, insurance company or one of the other bodies able to act as a trustee or custodian. A minimum deposit is usually required. You don't have to be employed to run an HSA although, if you don't file for Federal taxes, you cannot get the tax relief.
Put simply, this is a reasonable flexible and tax-efficient way of providing health insurance for yourself. But it has one key advantage. Although you cannot borrow against the money saved, you can make a one-time transfer from an IRA into an HSA, and the money from the account passes like a cash inheritance when you die. So unlike the usual health insurance premiums which are "lost", savings remain savings. The big question everyone who is eligible must ask is whether they want to self-insure. Obviously, if the savings are inadequate, the HDHP will potentially pay out. That policy is safety net but the coverage is limited. So you have to judge which works better for your family's circumstances. If you feel confident that there will always be enough available to pay for treatment during your life, this is tax free savings with you in control of the investment. But if you don't want to take the risk, a comprehensive health plan for the family may give you better peace of mind.