Final answer:
The health care program providing supplementary TRICARE benefits to Medicare for military retirees and their families over 65 is TRICARE for Life.
Step-by-step explanation:
The health care program that offers additional TRICARE benefits as a supplementary payer to Medicare for uniformed service retirees, their spouses, and survivors age 65 or older is TRICARE for Life. This program is specifically designed to act as secondary coverage to Medicare, providing extended healthcare benefits to those who have served in the military. It aids in covering the costs that Medicare does not fully pay, ensuring comprehensive health coverage for the eligible population that includes military veterans and their families.