The Tripath amp's outputs are configured in an H-bridge. There is no ground. If you measure the "black" output w/r/t the chassis, you will see that it is quite active. If you connect the two "black" outputs from the Teac together at the common ground connection of a female headphone jack, you are summing the negative outputs of the amp's two channels. From the standpoint of sound and amp reliability, this is a problem.
Since most of the energy in audio is in the low frequencies, and the low frequencies are most often in phase, you probably haven't damaged anything permanently. However, if you play a recording that has lots of high-energy, out-of-phase content, then you will end up with a lot of current through one channel's high-side mosfet and the other channel's low-side mosfet, via the "ground" connection on the headphone jack. Things could blow up.
The right way to drive headphones from a bridged output is to disconect the two "ground" leads from each driver at your headphone's plug so that you end up with 4 wires, the + and - leads from each driver. You then connect the headphones to the amp as you would a pair of speakers (except that you would add an appropriate resistance to each circuit).
Your amp willl thank you for it. Your noise problem should go away as well.
sluggo
ps Memory fades, but I believe there are 4-line 1/4" plug/jack sets which will work for this sort of thing. Don't think I've ever seen an 1/8" equivalent, though.
pps The tripath's output filter is tuned for a 4-6 Ohm load. Anything lower will cause the high frequency response to droop, anything higher will cause it to rise. The impedance of the headphones you're using is (I assume) much higher than 6 Ohms, and this will lead to a rising frequency response above 10k or so. To take care of this, you could parallel a 6 Ohm, 2 Watt resistor with each driver. The combined impedance will still be close to 6 Ohms, and you should have plenty of drive for your headphones.