The only way that works for me is using 2 monitor speakers separately. Means. 1 output from ASIO devices. And 1 output from your pc jack. In this setup you can play IRIG and other audio(youtube or video files) at the same time. Good luck.
I believe it's the sample rate. If you are recording at 48 KHz and your card is one of the basic ones it won't be able to switch between the two. So if you wanna use it to practice over a youtube video or something like that, just lower the sample rate of your daw to 44.1 KHz and that should solve it ;)