Hello there.
I aren't %100 sure where you're at with the GNU/Linux installation.
Disregarding the last part about getting Ardour to run, I will try and give you some pointers from my perspective.

Ok, have you read this article?
I didn't worry about the asoundrc file or the asound.conf file but the main points about the hdsp system are covered. However it is not apparently clear from anywhere that you need the firmware known as hdsploader, the configuration program hdspconf and the mixer called hdspmixer to get the multiface to function correctly. On top of that you need the hdsp module or compiled into your kernel, this is known as snd-hdsp

Hdsploader is in the alsa-firmware set of packages/programs/equivilent debian/ubuntu deb files. Hdspconf and hdspmixer, I think are in alsa-tools (possibly in alsa-utils, just get them both). Before you try and download the programs go through the steps below to see if they are already in your system. As you are using a multimedia-centric distro like Ubuntu Studio I expect the module to be loaded but perhaps you need to get the rest of the packages.

You may need to get them through synaptic if they aren't loaded already. I don't actually know how the actual packages are configured because I use gentoo and it works very differently to Ubuntu.
To see if the module snd-hdsp is loaded in your kernel; use the command lsmod to look for the it. If it is not there run sudo modprobe snd-hdsp to see if it is available but not loaded. If it is there, in a terminal try running hdsploader as a normal user. If all your lights flash and then disappear, then the firmware has been uploaded and all is working well. If the output of the terminal says there is no such program you will have to get alsa-tools or something similar. If it worked then as a user run hdspmixer.
Something very necessary to realise is that the inputs and outputs are muted if hdspmixer has not been run. Hdspmixer is a clone of Totalmix and although the shortcuts/quick keys are different it is essentially the same, so read that part in the manual (totalmix for windows) to figure out how to use it.

HTH