When you are in the vertical Portrait view select Hospital, which is under The World Bank and above PlayMesh. For those who know the PlayMesh model well it will not be a surprise that you will not even get a full interface in the Military Might Hospital if you are at full health. You will just get a condescending line that reads "You don't need the medic."
When your health has begun to dwindle, the Military Might Hospital will have a heal button the center with a cost above it. This cost will be different at different points in Military Might, determined with factors such as the amount of healing you need at the position you are at in Military Might.
At the top, it will list your balance at the Military Might World Bank. You must use the money you have in the Military Might World Bank to pay the bill in the Military Might Hospital. You are not allowed to use spare cash.