Early on up until the first Avengers they were, but that movie strained the relationship due to how much the DoD wanted to meddle in the production. They didn't like the helicarriers due to realism, for example. And you can see shit like F-35's on the flight deck, national guard doing their thing during the invasion, Captain America straight up using an M4, things like that.

After that movie, the influence the DoD had was much more subtle if it was there at all.