Audio monitoring w/ headphones through HDMI port
What you want is generally called an "HDMI audio extractor". There are several hardware products on the market that will extract the audio in the HDMI stream to an audio out connection and pass-through the video part.

A search on ebay gives you several results: http://www.ebay.com/sch/i.html?_nkw=HDMI+audio+extractor

Though if you need very high quality audio you probably need a more professional product with a good built-in DAC (digital to analog converter). HDMI audio is digital so it needs to be converted to an analog signal and the hardware used in these products isn't meant for high fidelity audio production. Or buy a cheap one with an digital output and use an external DAC.