HSA question – spouses

When my husband and I got married this year he got on my employer HDHP. He since has decided he wants to be back on his employers plan (only PPOs offered) when open enrollment hits. Unfortunately, my insurance runs July-June and his runs January-December. Since the open enrollments don’t line up and there is no QLE for my insurance I figured I would just carry him on my plan for the 6 months knowing it’s not really doing anything. His employer PPO would be his primary and my employer HDHP would be secondary.

My only area of confusion is with HSA and FSA. Currently, I contribute to an HSA account through my employer, my husband does not contribute to an HSA. When he is essentially double covered with a PPO and HDHP can I still contribute to my HSA or does that break rules? Also my husband cannot contribute to an FSA if I’m contributing to an HSA, right? Does it matter if we file our taxes MFS vs MFJ?

Because of our insurance years running at different times and him having a primary and secondary insurance for 6 months it is just confusing and seems unique to what I can find online.