You are only eligible to contribute to an HSA if you are covered by an HSA-eligible insurance plan. You can be covered by more than one plan (your own individual plan and a spouse's plan) but they both have to be HSA-eligible. If you have any "other coverage" that is not HSA eligible, you can't make contributions. "Other coverage" also includes an FSA account attached to your spouse's plan, because even if your spouse's plan only covers the spouse+child, the FSA by law covers the owner, spouse and dependents, so your spouse's FSA will disqualify you even if you are not a covered person on the main plan.
