How can I play DTS-HD and Dolby TrueHD through my home theatre system supporting DTS and Dolby Digital?

As far as I know you can't pass dts on analog cables. What you are probably doing is passing 2 or more of the already separated /processed channels to your home THEATRE system (which mean it doesn't really matter if it support dts or not). If you want to use your home theatre dts processor you need to connect a digital feed (e.g. the optic connector that i'm sure a 100$ sound card has , unless You spent those 100$ back in 1985) addition in reply to your added link: something is peculiar about your system, too many "outs" not enough "in"s are you missing any input jacks hiding on the fornt or other place on your home theatre system?

Using headphone jacks or RCA jacks, that's just stereo analog sound. There are three ways to carry a proper DD or DTS bitstream. Optical cables, coaxial digital (looks exactly like RCA jack, but digital, use any RCA cable) and HDMI.

So your sound system needs one of those inputs for this to work or you will only have 2 channel sound.

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