Yes. This opens a process called coordination of benefits.

The most common form of this is when you have a major medical plan (think normal health insurance) plus an indemnity plan (think Aflac). The indemnity plan pays you a lump sum when a certain event happens, such as going the emergency room. You can use this lump sum payment to pay the deductible or copayment that your health insurance plan requires for the ER visit.

Another example is when you have Medicare Part A and an employer-sponsored health plan. In this case, you have two forms of coverage for your hospital expenses. When you need care, the hospital will bill the insurance company first and Medicare second, resulting in a lower overall cost for you.