The military helped develop the technology, but they run their own "Internet" networks that are completely segregated and independent from the public Internet.

They helped with protocols and standards and such more than anything else. Military interest in Internet technologies relates to the ability to have redundant, interconnected sites so that if one site goes dark for any reason, the other sites don't lose their connection to eachother as a result. Obviously this world help with keeping the military operating and orders flowing in the event of an international incident where some of their sites are taken down or otherwise disabled.

The public Internet, while following similar models, isn't nearly as decentralized as you may expect. Almost all of the connectivity and data is warehoused in datacenters at, or near Internet exchange locations, or "IX"es. IXes and their locations are not secret and taking out a few IX sites is a good military tactic to disrupt communications, at least for the civilians in a country, which would create significant issues trying to keep everyone calm and safe. Almost all telecommunications today are Internet based, regardless of all other factors. The only somewhat decentralized civilian communication technology is radio, specifically broadcast radio (like FM), but even getting a message to an emergency broadcast FM station would be a challenge if the Internet was disabled, taking out phones (both cellular and landline), and all data communication. The only way to get an emergency message to an emergency broadcast station in that circumstance, would be to physically send someone there with a military communications system (generally two way radio), to relay the messages for broadcast to the public. There's enough FM stations and emergency broadcast stations that effectively disabling all of them is strategically difficult.

All of your communications, whether landline, cellular or Internet is basically all routed through your local IX before it can go anywhere; so if that goes down, you can kiss all of your methods of communication goodbye, unless, of course, you're a qualified amateur radio operator (or HAM).

Ham radio has a bit of an image problem as an obsolete hobby, but it really isn't. There's continual efforts to develop new and interesting wireless technology to run on the radio bands. Hams also have a network of repeaters and radio relays that can be brought online in geographically diverse locations for the purposes of enabling communication when commercial networks (like cellphones) become unavailable. Hams have saved lives and relayed critical information to and from first responders in natural disasters like hurricanes and tornados when all other communications have been disrupted.

But if you don't know how to use a radio, like a ham radio, then even having the gear is useless. The best way to understand enough to be competent in using a radio when it matters is to get certified. Unless you have, or seek that certification before there's a major incident, natural or otherwise, you may be shit out of luck when it happens.