Mulch is a wonderful thing but it isn't going to make a garden weedLESS, unless you are starting with weed-free soil to begin with. Some annual weeds, and pretty much all perennial ones (quackgrass, thistle, perennial sowthistles, bindweed, etc) will come up through really quite a lot of mulch, more even than is healthy for your garden plants.
However with the mulch cover on there, the soil gets much looser and more friable, and stays damper, which means that (especially after a couple years of this) it is much easier to pull out the weeds by their roots.
I have gradually got my front flowerbeds essentially quackgrass-free, and *almost* perennial-sowthistle-free, after 5 or 6 years of mulching and weeding. In a flowerbed you have to remember that significant-depth mulching will also decrease self-seeding of flowers, which in some cases is good (how much veronica or perennial flax do you *need*?

) but is also a little sad in a way, and sometimes inconvenient for things you *need* to self-seed.
I have to watch how deeply I mulch in the veg garden though because too much depth seems to encourage the voles/slugs/earwigs too much. And again, because my veg garden soil cannot by any stretch of the imagination be described as free of weed seeds/roots, it ain't weedless gardening, it is just "you weed less"
JME,
Pat