Compost is a multi-purpose amendment that improves the soil for better overall plant health with edibles and ornamentals alike. Since it is mixed in with the soil or layered on top of the soil before planting, you need only put the weed block cloth over the amended soil. If additional compost needs to be added after the weed block cloth or mulch has been installed, the weed block should be pulled back so that the soil gains all of the direct benefits of compost, including improved soil structure, better drainage and beneficial microbial organisms.
To gain the nutrient and some microbial benefits of compost without using the humus itself, compost may be soaked in water, then strained to produce compost tea. The compost may also be brewed, or allowed to ferment to make it even more microbially beneficial to the soil. This brew may be poured onto the soil any time before or after the weed block has been installed, since it is liquid and will filter through easily.
Compost with woody debris that has not yet completely broken down makes a fine weed block in and of itself, even as the nutrients leach down into the soil. However, using coarse compost as a mulch over a weed block cloth may encourage weed problems, since the weave of the cloth will keep even small and medium-sized pieces above the weed cloth, where they form a fertile bed for weeds. It's often better to use either weed cloth or coarse compost to block weeds instead of trying to use both.
Organic mulches as weed blocks are best to use with compost, since both materials add fertility to the soil. Well-composted soils are light enough to make weed pulling an easy task, and a layer of organic mulch such as bark, wood chips or pine needles above the composted soil will ensure that most weed seeds can't find purchase or can't germinate because they need access to sunlight.