That's an oxymoron for anything other than very low exertion levels. Breathable, waterproof fabric exists and probably works fine if you're walking but for anything more strenuous, Goretex or any other 'breathable' fabric quickly gets overwhelmed with sweat and all your clothes will get wet.

I've had much better success with jackets that have lots of openings to let air circulate, somewhat like a glorified poncho. I recently bought a J&G jacket for $100 and it seems to work quite well. It has large pit zips which I leave open and attach the bottom and top velcro without zipping up the front. If it's very cold and/or I'm not working hard on the bike I could do up the zips for some extra warmth.