What deductible does a baby’s birth expenses count towards?

Writing from Jacksonville, Florida (32223).

I’m curious both in general, and how these things work for us in particular. When family members are on the same health plan, is there generally a separate deductible for each, or do all of their medical expenses count towards the same deductible?

For us, my wife and I each have a separate insurance plan through our employers. When the baby was born a few months ago, we moved him over to my insurance plan since it’s generally better than my wife’s. But we just had the thought that if they’re on the same plan, and their expenses both count towards the same deductible (which my wife’s expenses certainly have surpassed), we probably should’ve kept him on there so the rest would be paid for by insurance.

Is that the case, and should we have kept them together to count towards the same deductible, or do they have separate insurance accounts with separate deductibles to meet and all that? And because I’m about to get a new job and my wife may get a plan from the market, will we need to get a separate one for the baby, or might he somehow be included in my wife’s plan?

Appreciate any help y’all can offer!