ASIO Driver only supports one application at a time

ASIO can handle more than one devices, but the soundcard has to support this, which means the drivers have to support this too.

Secondly, the program can request to use ASIO exclusively, and if that is the case, other programs can no longer claim the ASIO driver.

That said, I work closely with the developers of OpenMPT (music software) and know from experience that the WASAPI is as good, if not better than ASIO, because it is native to the OS and has very low latency, just like ASIO.

If you're sure the drivers installed are the ones from the soundcard and not the ones that come with windows (this is important) then look for a setting in the program which states: Use this device exclusively.

That said, I would still recommend using WASAPI over ASIO.