AFAIK, HDMI is the highest possible bandwidth carrying connector in any system. So in general, if a system is designed to give DTS passthrough over SPDIF, it must provide the same over HDMI.
I am not really sure about MINIX though. I never used it.
This is for quick reference:
http://www.avsforum.com/forum/90-receivers-amps-processors/1315890-hdmi-vs-s-pdif-audio-faceoff.html
Other FMs please share your thoughts.