My friends and I meet up on the weekend to play Hidden and Dangerous Deluxe. It's going pretty well and we're having a great time, but we were tired of having to keep an XP machine around to host a server. TechGremlin posted a fix here viewtopic.php?f=28&t=2645 that works, but I wanted to try to fix the game directly. I reached out to Michal Bacik, lead developer of H&DD, and he gave me the source code to the networking DLL. I disabled all of the calls to DirectPlayVoice, rebuilt the DLL, replaced the old one, and it works!
Whoever is hosting the game needs download the fixed DLL, which I have put here:
https://github.com/WJLiddy/HDDMultiplayerPatch/
Then, navigate to the H&DD bin folder (something like Program Files (x86)\Take2\Hidden and Dangerous Deluxe\bin), delete the inet2.dll that is in the folder, and put the new one you downloaded in its place. Run the game and you should be able to host a server.

EDIT 4/18/2017: Updated the link to use a github repo instead of google drive.