Insurance for baby?

I don't know if this is a dumb question or not, but I know nothing about insurance haha. My husband and I are both 24 and can be on our parents insurance until we're 26. Since both our parents have amazing insurance, that is the plan. I am also in dental school and when I graduate I'll be 26 so it will be good timing since I'll then have an employer and an insurance policy through that. But in the meantime, since we are both dependents and don't have our own policies, how does that work when baby arrives? I know usually you just add the baby as a dependent on your policy, but I checked with my insurance and I can't add a dependent to mine since I'm already a dependent. Can I just get a sole policy just for the baby?