I've made 5 of these so far and have tried different combinations; fleece on both outer and lining, fleece on only outer and nothing on lining, fleece on outer and interfacing on lining.
IMHO and it's only MHO, I like the fleece on the outer and a med. weight fusible interfacing on the lining and inside pockets, I also reduced the fusible on the handles because they stood at attention and I felt that they should be softer. For the handles I like half the fusible.