Franz,
The only thing I can suggest for this is to see if the different channels may be registered as different devices. Try them one at a time using the examples to record on different channels.
As I don't have (or have never heard of) a multichannel sound card, I can't advise you on the compatability with LabVIEW.
I can however suggest that a DSA card may be an option if this doesn't work. NI has some pretty good DSA cards with great resolution (16 bits and higher) and sample rates that are probably higher than the soundcard you are using.
If you don't have the budget, the quality is good enough, and you can get it to work, go for it.
Good luck, and please post your results. It helps everyone if we all know the answer to questions like this
.