I tried with weed barriers--thick ones, and 2 inches of mulch. It did not work--also due to at some places the landscape company that I had hired put less than 2 inches (The company thought 2 inches mulch plus weed barrier was enough) All the roots of weeds were growing under the weed barriers, and since the mulch has become soil, and I did not add more mulch, other weeds grew on top as well, and it was a mess. It took a lot of work to remove them, especially where I had added more shredded mulch, and all has become a thick layer of soil with lots of weeds.
From several lectures that I have attended, and also from books, the only way is to cover the areas that you want to be covered with mulch is to wet layers of newspapers (do not use shiny nor colored paper) or use cardboard (take out the plastic tapes, but most importantly is to cover the area with 6 to 8 inches deep of large bark mulch---the mulch will not turn into soil easily--- and you will have to add more when the mulch layers get thinner. It has to be at least 6 inches deep.