Nope.
While on active duty, the military member gets free medical care, and the dependents get some care free and some at very low cost.
After military member's time is up, if he or she gets an Honorable Discharge, the veteran can apply for Veterans' Administration medical services. They may or may not be accepted into the program, depending on the criteria that is met.
Military retirees can apply either to VA or get Tricare medical insurance (low cost).
Family dependents can be included in the Tricare coverage plan at relatively low cost but it's not free.