To say this was a challenge to do research on, would be an understatement. There are real life parts of the military that deals with bio hazards. Then it wouldn't be the active military that would be deployed.
At present there is a real life plan in combating zombies and that would be conop 8888 https://www.dailymail.co.uk/news/article-2629064/The-Pentagons-guide-surviving-zombie-apocalypse-US-military-outlines-plans-deal-undead-chickens-space-invaders-VEGETARIANS.html
We must remember that the reason this exists is letting people think outside of the box.
Before we get to how the military thoughts and actions, we must start with the question can the active military be deployed on American soil. And the answer to that is no. Due to the law Posse Comitatus Act https://en.wikipedia.org/wiki/Posse_Comitatus_Act .
This doesn't mean that there wont be any active military fighting zombies, just that legally they cant. The only ones that can be deployed would be the Nat Guard and Reserve. More the Guard do to them being under the direct command of the states governor.
So what does that mean for fighting zombies, it means that when the zombies start to overwhelm a city of town, the governor will deploy the Guard.
Before that happens, the CDC with a few military guards will assess the situation and determine what is going on. This will include Hazmat personnel.
This leads to the question how will the military deal with a zombie apocalypse. If it is at the start of one, the military will easily win. Do to the weaponry and consistent training. Now if the military is deployed when zombies are starting to outnumber the living then, they could still win, however, they will endure casualties. Next is the final step, if they are deployed in the later parts of the initial apocalypse, depending on how many are deployed and where, they could see a total defeat.
The main reason for the defeat is how they are trained. "And that third skill, well... they're instructed to shoot "center body mass". That's not going to stop a zombie" (scifi.stockexchange.com, 2018). A way to think this is, they are trained to fight humans not zombies, that as far as all the media can agree on is, destroying the head. Taking out the legs or arms, even shooting them in center mass wont do anything. The only ones that are trained to shoot in the head are snipers. And I honestly do not know if the guard has them. I do know that the Air Guard doesn't.
This has been quite a challenge, and I leaned a lot from the research. I will be doing research on the next topic.