I'm not familiar with your area so I looked on Google Maps. It appears that the only military airfield within hearing range of Madison is Redstone AAF, which appears to be a small AAF with just a few helicopters.
If I lived in your area, the first thing I'd do is get an antenna on the roof.
Next, I'd look on RR for Madison County > Redstone AAF and Huntsville Int'l for whatever milcom freqs are listed. I'd also check airnav.com for both locations. That should at least get you started with tower and App/ Dep frequencies. Then I'd look on-line for your local ARTCC frequencies. It seems to me that you stand a better chance of hearing high altitude transient military a/c than local traffic.
Lastly, I'd spend a couple of weeks searching 138.0 ~ 142.975 (You'll find that most comms will be AM, but some will be FM), and 225. ~ 379.975 AM.
I could be wrong, but my experience is that military helicopter air-to-air comms can be low band FM, VHF AM, and UHF AM.
Again, my experience is that most military helo's use VHF for ATC, as they fly low & slow and are surrounded by civilian air traffic.
Good hunting.
<>< Mike