When you receive the COBRA insurance election form, you will have an option to choose who you want to be covered under the COBRA insurance continuation of your group health insurance plan.  This means that you can choose to cover only your children, only your spouse, only yourself, or any combination depending on your needs.

You may want to consider who needs to keep the current health insurance plan under COBRA insurance the most (i.e. someone with a preexisting condition or someone who needs consistent medical care) and cover other family members on a less expensive plan.