If neither individual's HDHP plan covers anyone other then that particular individual, each of you has self-only HDHP coverage and each of you is separately subject to the self-only contribution limit, so you must choose self-only for the type of coverage (assuming that you have no disqualifying coverage such as Medicare)..
If your High Deductible Health Plan (HDHP) is a self-only plan, then you would choose self-only. You could also choose family if that is the type of coverage that you have in your name. Family coverage would mean that you and at least one other person (perhaps a dependent) is covered under the plan in your name.
The choice of self-only or family coverage will determine your maximum HSA contribution limit, so you do need to be sure to enter the correct choice to match your actual type of coverage.
If neither individual's HDHP plan covers anyone other then that particular individual, each of you has self-only HDHP coverage and each of you is separately subject to the self-only contribution limit, so you must choose self-only for the type of coverage (assuming that you have no disqualifying coverage such as Medicare)..