Are you aiming for extra absorbency plus a stay-dry liner? Or just extra absorbency?
If you're doing the extra absorbency plus stay-dry then the fleece/mf combo should work but just make sure the mf doesn't touch the skin - perhaps line the other side with a bit of flannel or something (retired receiving blankets perhaps?), especially if anyone else is doing diaper changes and wouldn't know which side is 'up.'
If you're wanting extra absorbency only, don't use the fleece, and sandwich the mf between something - flannel ought to do it.
I'm answering this from a sewing perspective as I don't use microfibre myself, but lots of people do.