If you are using the HD500 as your audio input device, then it must also be the audio output device. This is by definition of the ASIO protocol standard. Every true ASIO device/implementation requires this. So in your case, what you describe is exactly what I would expect: when using the ASIO driver the HD500 is both the input and output device, which is why you hear the output through your amp which is connected to the HD500 outputs. When you switch to the non-ASIO driver you can then assign the HD500 as the input device and your computer soundcard as the output device - but of course the sound quality is unpredictable because you are now mixing protocols, and the HD500 is designed to conform to the ASIO prootocol. I don't have any suggestions for improving the sound quality in this setup and I don't think you will have much success with that. Also, this setup is not supported by Line 6 and so you won't get any official help with that here.
I think you have 2 options:
- use the HD500 ASIO driver and learn to live with it being both the input and output device, as it is designed to be. This setup is supported by Line 6. You will get output from your computer speakers if you connect the speakers to the HD500 outputs (e.g., headphones). I highly recommend this setup for the best sound quality.
- use the other driver and also set your soundcard to be the audio input device. Connect the HD500 outputs to your computer soundcard inputs - do not use the HD500 USB connection. The sound won't be as good as the first option, but it may be better than you are getting now by mixing devices. I do not recommend this setup - the sound quality will be inferior because you are using your inferior computer soundcard.