Badger are the ones using non standard fitting, iwata use the same 1/8inch fitting that almost all other airbrushes use

the one that darefsky linked should fit the bottom of the badger brush to make it compatible with standard 1/8inch (or iwata) hoses and accessories
It sounds like the other end of your hose is a 1/4inch when you wanted 1/8inch, they sell those too, but you can use an adapter.
http://www.everythingairbrush.com/acatalog/Adaptors___Regulators.html
This set includes a 1/4inch male -> 1/8inch female adapter that you could attach tot he 1/8inch output of the compressor which would allow the 1/4inch female hose fitting to go on. ...
Personally
id go for the one that was linked in the above post, attach it to the bottom of the badger airbrush and use standard hoses from then on