Compost makes a nice top dressing, which is about the only way it can be practically applied in permanent plantings, perhaps aided by what cultivation or mixing into the upper soil can be done. But I wouldn't confuse that with the function of a true mulch, for which I feel most mature "compost" is poorly suited.

For permanent plantings top dressing with an inch of compost followed by a cover layer of a good wood mulch to a depth of at least 2" and up to 4" is a good annual treatment in most areas of the U.S. Some folks like even more mulch. In the hot humid south some of us do it twice a year (things decompose rather quickly). Just get the beds cleaned and tweaked first, apply any compost or other amendments/treatments you are making, then cover it with your choice of mulch.

Link below to Linda Chalker-Smith's Horticultural Myths page. Mulches are broadly covered about a third of the way down the page. You might find the article titled "Arborist Wood Chips" especially helpful. Compost is covered in the section on Soil amendments under Organic matter.

Here is a link that might be useful: TheInformedGArdener

Anything that covers the soil surface is considered a mulch. Personally, I think compost is a great mulch. It has a great dark, rich appearance - more suitable for perennials or a mixed boarder than the coarser bark or wood chips - retains moisture and insulates the soil just as well as any other organic mulch and it is a perfectly adequate nutrient source. Beds/plantings that are routinely mulched with compost seldom need any additional fertilization. Ever.

The ony drawback is that it is not particularly longlasting and it is also a pretty fertile seed bed for any weed seeds that might drfit in.

What ever material is used as a mulch can help retain soil moisture if that material is applied thick enough, a minimum of two inches although in my experience 4 is better. Since I seldom have enough compost to apply that much to any planting bed I most often apply about 1/2 inch of compost and cover that with another material.

I apply about four inches of compost to all of my beds twice a year. How much you need depends on your climate. My soil is fantabulous and in my fenced back yard, I don't have any weeds because the mulch prevents them from ever growing. I have a few in my front yard, but my soil is so loose, it's no problem to pull them. I make a lot of my own compost and buy it by the truckload. In my area, to fill up my pickup costs 16 bucks.

Buying enough compost, $18.00 per yard in 10 yard loads plus $25.00 delivery charge, to cover my planting beds 4 inches deep twice a year is cost prohibitive. Supplementing that compost with shredded leaves is much less expensive.