Linking Processing and Albeton Live is very possible, using JACK.

JACK: http://jackaudio.org/

With this installed, turn on JackPilot. Albeton (or any music interface for that matter) must be turned OFF. This fix won't be possible in iTunes to my knowledge (I'll talk about that later on, but anyways, let's carry on. This 'JackPilot' allows you to route connections between apps. Open Albeton, go to Prefs > Audio and select the output 'Jack Server'. This sends the Ableton output to whatever is on the other end, so processing. When this was written, Processing doesn't allow changes to where it gets the audio, so you'll have to go to Settings (or System Prefs or whatever) and set the default input to Jack Server. This connects up Albeton and Processing.


TROUBLESHOOTING:

No sound comes out of the speakers!
With Windows, you can tick 'Listen to this' (or something like that, I don't use windows) in System Settings > Sound > Input > Jack Server > Preferences, which, as long as the System Default output is set to Speakers or Headphones, should work.
With Mac, you can download a tool called LineIn, which does this for you.
With Linux, use this in the terminal:  pactl load-module module-loopback

I wanna use iTunes
Erm... You could use a manual approach. Use this setup of wires:

Headphones -> Splitter
Splitter -> Headphones/ Output
Splitter -> Line In

This should work fine.

Hope this helps.