I've read several articles talking about damp newspaper sheets under the mulch to help keep the weeds down. The reason it needs to be damp is so that you won't be chasing it all over the yard if there's a breeze before you get the job done!
One site states that a 2-5 sheet layer has the same weed-blocking ability as 2 inches of mulch.
Newspaper would certainly be alot cheaper and less mulch would be needed on top. Over time the paper will decompose, not like the plastic sheeting that's forever.The newspaper will not only hold moisture itself but acts as an added barrier to moisture loss.
Since we didn't have the mulch down yet, we decided to give the newspaper a try.We covered about a third of the bed with the paper, using 6 inch pieces of metal hangers bent in a v shape to hold the paper in place. Then we spread the mulch over top.
Time will tell if this is a good idea. I'll keep you posted.