You need the Zune software to stream Zune content, and per the system requirements, it's not supported on any version of Windows Server (which would include Windows Home Server). I believe some people have managed to get the software to install, but then you need to contend with the headless nature of Windows Home Server; normally there is nobody logged in to the server interactively, and the Zune software is likely to require that.
You could try asking over on the Zune forums; you'll probably get a lot more Zune-specific help there.
I'm not on the WHS team, I just post a lot. :)