HSA

HSAs are individual accounts.  It doesn't matter who makes the deposit, any money someone puts into your HSA is your contribution, not theirs.  For any individual to make a contribution, the contribution must be made to that individual's HSA.

eligibility requirements for HSA

1) must be covered by HDHP

2) may not be covered by any non-HDCP  - insurance for only dental or vision coverage is ignored

3) can't be enrolled in medicare

self-employed

an eligible individual or any person including family member may contribute to that individual's HSA

Married couples.  

if either spouse has family coverage both are treated as having family coverage.

if family coverage the maximum allowed contribution can be made to one account or both spouses may have their own a/c with the maximum contribution split anyway they desire.  each spouse that has an HSA a/c must file form 8889.  even if you choose separate a/c's, the money in the account can be used to pay the qualified medical expenses of the account beneficiary, their spouse or dependents.

if neither has family coverage and both are covered by HDHP, each must have their own HSA.