Straw to 6 inches on a carboard base should discourage and stop weeds. Are you mulching around the planting beds--such as paths--or in the beds? In the planting beds a straw mulch of a couple of inches once plants are established and the ground has warmed (but don't mulch right up to the stems). Or, you could "lasagna" garden: lay down the cardboard, then one or two inches of straw, then an inch of topsoil, then an inch or two of straw topped with aged manure, then another layer of topsoil and then plant.

Here is a link that might be useful: HarvestToTable.com

is this using straw on top of cadboard as mulch around the plants in the garden?

if so with perennial type gardens it may be fine, thugh the cardboard itself will act as a water shed in this case. for around vege's i think i'd leave the cardboard out (use that before mulching around your fruit trees say or when building a new garden.

mulch for us means at least 6"s and up to around 8"s, we regularly use green type mulches instead of straw though straw does last longer it is also more expensive. the hay type mulches we use also add many nutrients as they break down.

len

Here is a link that might be useful: lens garden page