Have you got Biab ASIO set to Always On ? as it won't release it when stopped.
But yes, VoiceMeeter Banana gives you 2 ASIO Devices

I have VoiceMeeter Banana Hardware Out set to my Audio Device.
I have Windows Playback Device set to HiFi Cable or VB Cable both available from the VoiceMeeter website,
you can set the Hardware Input 1 to HiFi Cable and Hardware Input 2 to VB Cable

Reaper is Using VoiceMeeter ASIO AUX, Biab is using VoiceMeeter ASIO the VoiceMeeter Mixer mixes all the ASIO and non ASIO out to the Hardware Audio Device/s.

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