Deciding on double coverage

I am starting a new job in a hospital next month, I can get an HSA plan through that job for our family (2 adults, 4 children). Medical, Dental, and vision would come out to about $350/paycheck if I went with the maximum contribution to the HSA (employer also adds $1400/annually). I’m not sure specific costs for each service, though.

My husband’s employer covers health and vision insurance, but dental is not included. We have Kaiser currently, but he does have the option to switch to Blue Cross. The way they explained the contribution to his insurance was that it’s related to hours worked, Blue Cross requires more hours than Kaiser. Nothing comes out of his checks though, when I checked the Kaiser paperwork all it says regarding premium is that his group is responsible for paying it.

I guess I’m just not sure if he should switch his coverage to Blue Cross since the network would be a lot of the same providers as the one I would get with the job I’m starting, or if he should keep Kaiser. I’m not entirely clear how double coverage works, I did see someone mention that if there is a low premium on the spouses insurance then you couldn’t contribute to an HSA, but I’m not sure if his is considered low premium since his group covers it.