I made up a set of four burp clothes for my Sister- in-Law's baby shower last weekend. Just recently I saw some simple burp clothes that were backed in fleece. I'd never seen that before, but I love the added cushion that the fleece gives to the burp cloth. I, myself, have rather boney shoulders. I think that every newborn baby deserves a nice cushy shoulder to rest their head on.
To make these I used this basic tutorial from Oopsey Daisy to create the template for the burp cloth. I then cut out one layer of cotton, and one layer of fleece. I placed them wrong sides together, basted the raw edges, and serged around the whole thing.
Now if you are a patient person, and like to crochet around burp clothes and receiving blankets, that could definitely be applied to this project.
I ended up quilting the burp clothes just for a little added reinforcement and detail.
Because you're working with two different materials, I'd recommend pre-washing all of your fabric on this project.