Would the military help in the event of a zombie apocalypse?

They'd have no choice! Just because they're military doesn't mean they can't be attacked. The military actually have various plans for if aliens attacked, I think they probably have a zombie plan that they don't admit to. It would be to contain the infection (like on all the movies) the problem with the military is they are just people. When it looks bleak the army would likely desert the people they should be protecting.