They don't for full-time regular force members. There are insurance programs available—for example, SISIP, the service income supplement insurance program—but for their care, so long as they're members of the armed forces, any element of their health care would be the responsibility of the defence department. Some of it might be provided by a third party, but the cost would be the responsibility of the defence department, and arranging for the care would be the responsibility of the defence department.
On April 8th, 2014. See this statement in context.