If you had the C-section, the medicals should already be covered by his employment and insurance coverage at the time of the C-section.  However, any medical appointments for follow-ups, or for your child (you only have a certain amount of time to get your child on as an added insured) may not be covered should your husband choose to leave now. If there is no immediate rush or if he will be going to a new company, I would make sure the insurance coverages cross over so you are protected.