But it's really awfully complicated -- often the baby gets a separate bill too to muddle the waters. The ACA ("Obamacare") set a cap on in-network yearly out of pocket payments on family plans which, if memory serves, was around 11k in 2017. A complicated birth can hit this! Consider the costs of NICU, for example. (Oh and if an NICU nurse reads this: thank you, thank you, thank you for the life of my niece.)
As to what the insurers pays, I do not know.