Hi!
I've been searching for a good solution to this for a long time (on this forum as well), but wasn't able to find anything that would work reliably - until today.
I stumbled upon Asio Bridge from vb-audio and, together with ReaRoute ASIO driver I can now e.g. listen to youtube while a Reaper project is playing!
I'll be posting this on several different forums so I wrote how I configured everything in a doc to avoid a lot of copy-pasting. Please let me know if you tried this and whether it worked for you.
Instructions:
https://goo.gl/JYez2i