Last year I put just chippings down on my pathways and found that the weeds eventally came through just as thick and fast. Always one who prefers something for nothing - rather than buying membrane, I found large strips of tought plastic bagging (I was lucky enough to find some unused bags at work on a roll which we cover kitchen products, but something like compost bags will work). I put small holes in it for drainage, before covering with chippings (delivered free by our local council gardening contractor).
This has worked fine. The only thing is a few blades of grass seem to be working their way out between the raised bed and the pathway but so few its not worth worring about.