Per 16CMS 8.1, "Chicago's preference for the 'down' style" is evident throughout Chapter 8, from 16CMS 8.1 through 16CMS 8.197.
Yes, there are that many rules on the question of to caps or not to caps.
But here's the gist in general: you do not capitalize unless it is a proper noun (a person's name or a place like a city or whatever, so something found capped in Web11, for instance). As for the army, navy, air force or marines, as you can already see, do not capitalize those references unless you are using their complete name, as in United States Marine Corps for example. 16CMS 8.111.
Another place where I see confusion in manuscripts is when to capitalize references to Dad, Mom, etc. Read these examples and find the distinction:
"Hey, Dad, come here please!"
"I'll see you later, Mom."
"Peter, get that room cleaned up now!"
"But, Mr. Smith, this is my first day."
"My mom can beat up your mom."
"His dad is some powerful CEO or something."
"I think my grandmother is due to arrive tomorrow."
"The dad on the far left in this picture is Timmy's father."
First, as evidenced in the initial four sentences above, when you are getting someone's attention, using their name to call out to them, to direct your conversation their way, you use caps for Dad, Mom, and of course with a person's real name.
Second, as in the last four sentences given above, anytime there is an article (the, my, a, an, etc.) or a possessor (my, his, your, our, their, etc.) that precedes a generic noun, then the down case is the way to go.
Denise Barker, author + blogger + copy editor