Thank you for your replies.
1. Drivers - I downloaded INSTALL U-MIX44 1.0.4.ZIP file. Installed without any issues. However, as I mentioned Windows 7 still uses Microsoft driver when I go to the properties in device manager. Not sure if how it suppose to be.
2. boc - yes, we have the same problem. The thing is I don't want to use built-in card. The whole point of paying 100$ for U-mix44 is to be able to enjoy a quality sound card in every application.

I didn't buy it to listen to youtube videos

3. christiankoopmann - Thanks for your advice. I don't have any other cards on my machine - built-in card is disabled in the BIOS and I uninstalled built-in card's driver from Windows. So yes, U-Mix is a default device and it it the only sound device on the machine.
I also disabled Windows Sound scheme. It didn't help.
Side note. Second Life sees the card, I can view it in the properties. The same goes for MediaMonkey - I can see the card when I go to configure Output plug-ins. Neither one produce any sound though.
thanks, Ilya