Not so in my experience.
Every call that I received from over there was a collect call which originated from the Base where the Troop was stationed. In my case it was generally a collect call from Georgia, and the cost was a pittance.
Call originated in Iraq, but charges only from Georgia, the military carried the freight from Iraq to the USA!
Not all facilities have that, and those that do have a limited number of lines available. often, you have to sign up well in advance. Most of the Army, Air Force Exchange Service (AAFES) outlets sell phone cards for the troops to call home using these cards.
This is from personal experience, as I have lived in several different countries over the past 35 years. So, please don't discourage this poster from proving phone cards or cash donations to a Chaplains office or military outfit that could provide such a service.