It depends. If there are just the two of you, you are 'primary' on your own policy, and your spouse is primary on his/her own policy. By default you would be 'secondary' on your spouse's policy. If the two of you have kids, you can elect either of the parents' insurance carriers to be primary, but you must do this officially, by filing the proper records with the carrier who you want to be primary. Typically, you need to decide which policy will be primary for the kids each year, as you will need to add the kids to one of your policies. You make this choice by reviewing both policies' coverages, copays and costs. The other policy, by default, then becomes secondary. If you just had a child, you should call your human resources department and/or health insurance company to work out the details and get the child properly insured.