You should be able to able to quilt through the foam without any issues. You want to use a Microtex 90/14 needle
Here is a tutorial on quilting foam. We made this bag in class using one layer of bosal.
https://www.youtube.com/watch?v=zIWtJ_BVD0c
I didn't realize that you mentioned foam in your original post. I was thinking of the stiff stabilizer like Pel-tex when I replied about making 2 separate pieces. Good luck!
You can simply make the quilt sandwich, then quilt and bind as desired.