This comes up every few weeks it seems - it just doesn't work the way you think it works. You don't assign an interface to an application.
An interface is used to access networks it has routes to, or if both set as gateways then whichever has the better metric would be used.
Now you could setup your browser to use a proxy - and then setup a route to use which interface you want to get to the network the proxy is on. Now browser would use that interface.
I don't know of any applications that allow you set which interface to use.. So while you can split up traffic base on route, what your trying to do doesn't really work out. Because what network would you be browsing too - random. And if your talking p2p for download, again that would be random so difficult to setup routes to all those networks
So you could setup one as your default route, and then setup the other for some proxy your browser or download app uses -- which whatever network that proxy is on route through the other interface.