5.1 sound via HDMI?

My current audio receiver does not support HDMI.  So, I currently have HDMI from the STB -> TV, and optical from STB -> Receiver.

The downside to this is I have to switch inputs on both the TV and the receiver when using a source other than the STB.  I will soon have a new receiver that does have HDMI.  My planned connections then are:

HDMI STB -> Receiver

HDMI Receiver -> TV

Does the HDMI signal coming out of the STB support the same digital audio signal that the optical outputs?  Or is it 2-channel only?  Some of the threads I have searched indicated it might only support 2 channels, but they were also a little older, so I wanted to ask.

Thanks