If the DAC has multiple inputs (mine has USB, four S/PDIF connections, and two analog connections) then you would just set one of them to the default system output, and use another in Media Center.
That way both can be playing sound at the same time, and you just change input on the DAC to switch between them.
If that's not an option, to have system audio (web browser, games, other applications etc.) and Media Center able to play audio at the same time, you would have to disable Exclusive Mode in Media Center's device configuration or switch to a non-exclusive output like DirectSound.
With WASAPI in a non-exclusive output mode, the player must resample the audio to match the device settings in the Windows Sound Control Panel.
If you use DirectSound, Windows will automatically do this resampling itself, rather than the player.
So you get "bit-perfect" audio at which ever sample rate the device is configured to, but any other sample rate must be converted. DirectSound is easier to set up, but I'd rather have MC handle the resampling.