If you are ordered by a court to pay health insurance, then yes. But usually any such order would say you have to "provide" health insurance. Absent a court-order stating how much support you must provide, you must comply with the terms of AR 608-99 with regards BAH and support of family members. You should consult a legal assistance attorney on base for further info.
This post is for information purposes only and does not constitute legal advice, nor does it establish an attorney client relationship with Mr. Cassara.
Assuming that you are indeed active duty and have put your child into DEERS as a dependent (the JFTR covers what a "dependent" actually is, but if you're talking about health care and deductions, odds are good your child meets the definition), the health insurance should flow through TriCare prime without incurring additional premium cost to you.
As Mr. Cassara said, a base legal assistance attorney should be able to clarify things for you, but the health care issue should be easy to address.
Your obligations are listed in AR 608-99 but you must also comply with your state obligations, ie stare court order; see your legal assistance attorney.
This information is intended for public use only, it does not form an attorney-client relationship and it does not constitute legal advice. If you seek legal advice on military law issues, contact an military law attorney. My contact information is email@example.com or 804-955-9867.