The weeds are going to be very shallow-rooted and easy to pull. Just spend a bit of time pulling and problem solved. Or, more easily, you can take a rake and muss up the mulch; this will dislodge the seedlings and they'll die pretty quickly. Of course, something like dandelions or grass is going to require pulling, but still shouldn't be difficult if there is a good layer of mulch down. Don't make it harder than it is :0) (and no need to revert to chemicals)

How thick is the mulch? A good three inches should do the trick!

I always put down a layer of newspaper (and wet it) before I mulch - about 6 to 8 sheets - making sure to place it a few inches from the plants. This helps keep down the weeds growing through the mulch. The newspaper breaks down of course, so you have to do this every year (or perhaps twice, if you mulch in spring and in fall) before putting down new mulch. If your area is small enough, you could rake up the mulch and lay some paper down and remulch. Otherwise, as mxk says, use a rake or "claw" (just what the heck IS the name of that tool? :) I can't live without mine!) and cultivate lightly and the weeds should come out easily.

Just yesterday I finally had some time to do some work in the vegetable garden. It's been very dry here, and I thought my newly planted cukes and tomatoes needed some mulch. I didn't get to shred as many leaves as I usually do last fall (my mulch of choice), and had nothing on hand, so I cut up old leaf bags, ones which the bottoms had rotted on anyway (I re-use these things till they literally fall apart), laid that down, and then mulched with shredded paper. Doesn't look too pretty, but one is so blinded by the sun boucing off the white mulch no one can look for long anyway, lol!

In my experience when I formerly used shredded wood mulch or now just using shredded leaves, weeds are going to germinate and start growing on top... Regardless of what's below the mulch (soil, plastic, landscape fabric). These are easily pulled or you can use a variety of tools to ruff up the mulch and expose their roots to the air. For me the only weeds that would work their way through the mulch from the existing soil are dandelions. Organic mulches just reduce the weed count and make weeding easier.... But the don't elimate them.

Thanks, everyone. Will just plan on a little weed pulling time after work....will replace a workout that evening :-).
Mxk3 and Diggerdee - I especially like the rake idea, too!