According to
https://azure.microsoft.com/en-us/docum ... gurations/ , It doesn't look like Azure IoT Hub is supposed to work with Mono on Raspbian. At a guess, the assembly Microsoft.azure.device.dll makes a direct API call to Windows that just doesn't work under Mono.
Strictly by the docs, you can write the device-side part of your code in C, Java, or JavaScript to run on Raspbian, or in .NET if you instead install Windows 10 IoT Core as your OS.
You *might* be able to get it to run under Mono somehow (it might just be a matter of copying some missing files over from a Windows install but it also just might not work, period), but it'd be an unsupported configuration. It appears there are also some Python bindings, but for whatever reason they're not listed as tested on Raspbian (as Python works on Debian, my guess is there's a good reason why they haven't gotten it working Raspbian rather than they just haven't tested it, as it feels like trying it and adding it to the list would be pretty easy if it just worked.)