Maybe it's more obvious when named this way, but I don't think I've ever been under the impression that the DoD is focused on peaceful means of keeping the peace.
You're right. USAID was the Department that used peaceful means and encouragement for suffering countries in spite of lack of resources, adventurism, health and wealth inequalities and border disputes. It was a stick and carrot way of influencing participation in the spread of democracy, feeding the hungry and warding off disease that could spread to the rest of the world.