I live in the Washington DC area, and it gets pretty hot+humid here in the summer too. As Eon says, get yourself a quality mesh jacket (and maybe mesh pants too), and you’ll thank yourself. They do a great job of passing air through when you’re in motion, and at least letting heat escape when you’re not.
I have a Fieldsheer High Flow jacket, and it does a great job. CE-rated hard armor all around. Not a lot of pockets unfortunately. I wear it with Fieldsheer Titanium mesh pants (they zip together) for a good balance of protection and comfort.