It's your HDHP insurance that is either self-only or family, not the HSA accounts. HSA accounts are owned by only one individual.
And individual can have and contribute to multiple HSA accounts. With family HDHP coverage at at least one of the employers, the family-coverage contribution limit applies and the total HSA contributions to all of the HSA accounts is not permitted to exceed the family-coverage contribution limit (plus the HSA owner's catch-up contribution to the HSA ower's account if age 55 or over). If both spouses are HSA-eligible and one spouse has family HDHP coverage, both spouses are treated as having family HDHP coverage.
