Pub. 969 is a good resource for things HSA. For an IRS publication, it's reasonably readable.
E.g., on p. 4: "Family HDHP coverage is HDHP coverage for an eligible individual and at least one other individual (whether or not that individual is an eligible individual)." That seems to fit your situation perfectly.
If you have family coverage, you may contribute the family maximum.
Just make sure your spouse has zero money in any general purpose healthcare FSA. Even though her insurance policy doesn't cover you, by law FSA money can be used to reimburse a spouse's medical expense and that would make you ineligible for an HSA.