Firstly, an HSA account is only owned by one person.
If your husband has qualifying HDHP family coverage, he can contribute up to $6750 plus $1000 catch-up. He can't contribute an additional $1000 catch-up for you because the account is in his name only.
However, if you have no insurance other than your husband's qualifying family insurance, then you are deemed to have qualifying HDHP family coverage and can open an HSA in your name. (If you can't use the bank your husband's company uses, you can shop around for another bank, try to get the lowest maintenance fees you can find.)
Then if you also have an HSA, your family maximum is still $6750 plus catch-up, but you each get a separate catch-up provision. The $6750 can be divided any way you want but the $1000 catch up is specific to each person.
So, he could contribute $7750 (employer plus employee) and you could contribute $1000 to an account in your own name by depositing after-tax dollars. Or he could contribute $5000 ($2400 employer plus $1600 employee plus $1000 catch up) and you could contribute $3750 ($2750 left over of the family maximum plus your $1000 catch up).
His employee contributions by payroll deduction are captured on his W-2 and counted as "employer" contributions (he agrees to a salary reduction and the employer contributes the money.) When the program asks you for additional contributions, only enter your out of pocket contributions not made via payroll deduction (yours, plus his if he makes any contributions that way.)
Also in turbotax, make sure you enter that you have 2 separate HSA accounts in different names and be observant to where you are entering your numbers. You will say that you had qualifying family insurance even if it was only through your spouse. On your final tax return you will have two copies of form 8889. (If you see any references to internal worksheets, form 8889-T is for the taxpayer who is named first/top on the form, and form 8889-S is the spouse's form.)
If you have separate single health insurance that is HDHP and qualified for an HSA, then the limit in your personal account is $3350 plus $1000 catch up. The overall family limit is still $6750 plus catch up, but having a single HSA instead of a family HSA limits the ways you can divide the contributions.
And, if you have separate single health insurance that is not HDHP and not qualified for an HSA, then you can't make any contributions and his contribution limit is $6750 plus $1000 catch up. You can't use your personal $1000 catch up if you aren't eligible for your own HSA.
I was actually on the phone with someone from TurboTax when your answer came in, because I had called with a question about a problem with the website itself, but she ended up turning me over to a tax professional.
I had read elsewhere (on top of the 10 pages I printed out from IRS.gov) that he and I could *both* set up separate single accounts and take $1K catch-ups for all three. Don't know if that's legit and not particularly looking for every loophole. At first Kelly, the TT woman with whom I just spoke, said I couldn't do what you said, then, when I started reading to her from your first reply, above, she said I could but still left me befuddled.
If I open a separate HSA in my name, will the one in my husband's name still be a family account? I'm assuming that if I open an HSA in my name, I'm the only one who can use the money from it. Will I also still be able to take distributions from his?
If I open my own with $1,000 after-tax dollars, will that amount be deductible when I file because it's catch-up, even if I don't (probably can't) add anything else for 2017?
If your husband has qualifying family insurance, then both HSAs are considered family HSAs, but they share the overall annual maximums.
Anything that you or your husband contribute out of pocket is tax deductible on your tax return as long as you keep to the individual and overall limits. You each have an individual limit of $7750, and a family overall limit of $8750.
Distributions from either of your HSAs can be used to cover qualified medical expenses for either of your or your qualifying dependents, if any.