This production agreement between the Department of Defense and Nautilus Productions LLC is relatively typical, from the handful I have seen, and so provides a useful benchmark for how the DOD-Hollywood relationship works. It is very similar, for example, to the equivalent agreement for Battleship.
The first US attempt at Godzilla in 1998 included assistance from the US Marine Corps, but they declined to be involved in the reboot. Fortunately for the makers of ‘Nautilus’ (the working name for Godzilla at the time this document was drawn up) three other branches of the DOD were happy to oblige. The Army, Air Force and the Navy – primarily the Navy – appear throughout the film and lent men, equipment and lengthy technical expertise to the production. Retired marine James D Dever of 1 Force Inc. provided additional technical consultancy, particularly in training the stunt performers for the HALO jump sequence.
The resulting movie features an awful lot of the US military and not a lot of Godzilla himself. A total of 11 minutes screen time was devoted to the king of monsters. After fruitlessly firing thousands of rounds of ammunition and engaging in a lot of pointless messing about with a nuclear bomb, the US military doesn’t come across as heroic, competent or even useful but it seems they were happy enough with that depiction to lend the film numerous vehicles and other large-scale support. Indeed, if you look at the film’s credits then it is no surprise the military got more screen time than the eponymous monster hero: