I mulched my vegetable garden this year. I never did that before. It was the best thing I did. I had no weeds. Now I want to know what to do with the mulch because I want to prepare it for the winter and I have two compost bins from the summer. All the plants are out.
Yes, you can compost your mulch, keeping in mind your ratios of brown and green in your compost bin.
Here are some links with more information.