Using a HDMI Splitter before an AVR and Display
Due to the way that HDMI handshaking negotiations take place between source and displays or AVR devices, the display (unless it can accept multi-channel audio and has a setting for such) will communicate with the source to only output 2.0 channel stereo. This is due to the fact that in most cases an HDTV only has 2 speakers.
When using a HDMI splitter or distribution amp (DA) effectively you have 2 display devices competing for the source to send them the audio signal format type that they prefer. The technical rules of HDMI dictate that the lowest common denominator always wins that battle. The logic being that this rule should result in the maximum number of display devices functioning in some way. (i.e. a 7.1 capable device should still be able to output 2.0 channel stereo also, meaning both displays have picture + sound)
Unfortunately, what you and a lot of people really want from HDMI is for a mix of audio formats to be delivered from one source, which is just not possible currently.
Some splitters including ours can be pre-loaded with firmware where the highest denominator formats win the battle, but of course that would leave your 2.0 capable HDTV without sound.