Double-check me on this, but my experience is that HSA-ideas are unrelated to HDHP-ideas. So I would imagine that regardless of who is on your HDHP, your HSA capacity will be determined by your family size. Bottom line on simple eligibility is whether the HSA-person has any other forms of coverage --rest of the family doesn't matter.
You should also check with your HDHP on how expenses apply to your deductible when you're doing COB with your spouse's insurance as primary. For my plan (and this is super weird!) even expenses that are fully covered by my wife's (primary) insurance will favorably apply to our family plan's (secondary for wife) deductible. So if she has a major surgery on 1/1/2017, and her insurance covers it 100%, then our family's deductible for the year will be met right away. (But if we had already met the deductible on the family plan, then the surgery would not have caused a payout from the secondary/family coverage --so timing matters a lot.)
It is absolutely crazy that it works this way, so I wouldn't expect it to work in all states or all plans.