I have Dell Laptop (I5 and Intel onboard audio) and AMD on board chipset based desktop. With Linux, I can only get Stereo out of HDMI. If HDMI is working for you, I can port driver code to the hardware that I have.
You need HDMI 1.3. It is mostly a hardware limitation, rather than drivers.
No, its a software issue. Same setup works fine with Win 7 and sends not only 7.1 but 7.1 as HD Audio ( DTS HD MA). Hardware is HDMI 1.4 on all devices (Laptop, AV Receiver and TV).
Let me know if you come across any hardware on Linux that can do 7.1 channel audio via HDMI. I can port relevant drive code for the hardware that I have.
-Shamit