Don't know the exact differences between a P8H67-M and mine, which is a P8H67-I PRO but I also am experiencing the exact same problem.
My situation is as follows:
* TV: SONY KDL-40V5500 supporting 3 HDMI inputs, VGA (PC) and some old crap 
connections.
* AMP: SONY BDV-IZ1000W
* Mainboard: ASUS P8H67-I PRO (it has 3 video outputs: HDMI, DVI, VGA)
* Memory: 2 GB
* Video: Intel HD Graphics 2000 (Core i3-2120)
HDMI audio and video connects to TV through the amp (because the TV cannot pass signals newer than Dolby Digital 5.1). It is connected to HDMI1. The DVI and VGA connections are not used.
This system was built several months ago and Media Center has been working on Windows 7 Ultimate without even a glitch giving a great experience. All audio formats work well.
Now on to the Windows 8 horror. 
I was very pleased to see that everything worked smoothly,until I installed Media Center.
Running Media Center in full screen does 2 things as far as I found out so far:
1. It messes up the inputs of the TV (at least the HDMI ones)
2. It sends Media Center output to the VGA output (which isn't connected).
If I connect a VGA cable between my mainboard and the TV and then switch to the VGA input on the TV, I see media center running perfectly in full screen on that input.
If I ALT+F4 out of Media Center the VGA connection gets killed again (most of the times), but returning to the HDMI input still shows nothing. Once I switch of the TV (and implicitely the amp) and switch it back on, my desktop is once again showed on the HDMI input. Sometimes it is enough to switch to another HDMI input which has nothing connected and *then* switch back to HDMI1.
I have been mixing and matching with several driver versions but am currently "stuck" at Microsoft's latest WDDM drivers provided by Windows Update.
Before someone starts suggesting it: switching to VGA is not an option, because I lose all audio and HDMI appears to be a lot crispier.
Hope this helps investigating the problem further.