Here's a couple more things you should know.
The HSA account is only ever owned by one person, like an IRA. There is no such thing as a "joint" HSA.
To contribute to an HSA, the owner must be covered by a qualifying high deductible health plan and have no other medical coverage (certain limited exceptions apply). The amount the owner can contribute depends on whether they have single or family coverage.
However, because your spouse has a family HDHP, that means you are also allowed to contribute to an HSA in your own name as if you had a family HDHP insurance (as long as you don't also have some other form of disqualifying medical coverage). Your overall family limit is still $7000 (or $7100 for 2020) but you can divide that any way you want. For example, your spouse could contribute $5000 to an HSA through his work and you could contribute $2100 to a private HSA.
There are many banks that will allow you to open private HSAs, although they may charge a monthly maintenance fee. It is slightly more tax-advantaged to contribute through work, since you save social security and medicare tax as well as income tax. However, there might be other reasons why you would want to split your money up in separate accounts.
If you or your spouse is age 55 or older, you get an additional $1000 "catch-up" contribution allowance, but this must be contributed to your own HSA only. In other words, if you and your spouse are both over 55, your overall family contribution limit is $9100 for 2020, but your spouse's personal limit is $8100, because your catch-up amount can only be contributed to an account you own in your name.
