Unfortunately, while COBRA gives you the right to *continue* the former policy as it existed at the time you left employment, it does not give you the right to add to the policy, change the policy, etc. Since your daughter was born 4 months after the policy, if you needed to make a change to the policy to add coverage from her (e.g. go from either a single or married, no children plan to a "family" or "dependent" plan), they would not normally have to make that change.What is possibly in your favor, however, has been that you say you have been paying premiums for her already. If they have accepted the premiums, they may therefore be estopped, or prevented, from denying coverage at this time. Since you have paid premiums and therefore may have rights to coverage, you should consult about your situation with an employment attorney, who can advise you of your rights and recourse in this specific situation. Good luck.