I'm no audio expert, and I'm using Windows 7 and WASAPI. Nevertheless, if I explain a bit about my configuration, it might point you in the right direction.
I have two zones—one for my desktop (onboard sound) and another for my stereo (S/PDIF connection). This is necessary not only because they are two separate outputs, but because they are fundamentally different—and need to be configured differently. In both of them, I've set the Output mode to WASAPI. You would select ASIO. For the desktop zone, I've set the Device in Output mode settings to my computer speakers. For the stereo zone, I've set the Device to digital output (i.e., the sound card's pass-through to the S/PDIF connection). You should have the equivalent devices available in your ASIO settings. I'm assuming, of course, you do actually have a digital connection (S/PDIF or HDMI) to your stereo.
The next step is the DSP & output format settings—again, separately for each zone. These, too, are critical—in that you'll get no sound if they're not set correctly. You may need help from someone more experienced with your situation if that's where the problem lies. In the meantime, let us know what kind of stereo connection you have, your Output mode settings, and the results.