Thanks for the reply Razbo and I know what you mean. Many times I managed to get something working via trial and error and once it was up and running you just don't care anymore. I did already check in the sound recording options, etc., but until now no luck. I am sure there must be a way, but the reply from the Support of Behringer put me off a bit. He stated that you need to connect either a headphone or an amp for using the iAXE629.
Are you using the iAXE as well?
As mentioned under the edit I have an amp in my car now, so at least I can start hitting the first strings when I get home. Maybe in the next few days I will dive into the Device Manager again to try some more.