"Family " plans refer to whether the deductible on the high-deductible health plan is individual or family.
From Treasury's Q&A:
Can couples establish a “joint” account and both make contributions to the account, including “catch-up” contributions?
“ Joint” HSA accounts are not permitted. Each spouse should consider establishing an account in their own name. This allows you to both make catch-up contributions when each spouse is 55 or older.
Must couples open separate accounts?
If both husband and wife are eligible to contribute to an HSA, they are both eligible to establish separate HSAs. However, if both spouses want to make “catch-up” contributions when they are age 55+, they must establish separate accounts.
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