A bat is not a mouse with wings, and it is also not a bird with fur and teeth. A bat is in an order of its own, Chiroptera, which in Latin means "hand-wing."
In looking at the anatomy of a bat we notice that the wing structure is made up of elongated arms with four elongated fingers and a thumb.
Between the fingers and also connected to the body, back to the tail, is a thin skin membrane. This makes up the bat wing.
Most bats have the skin membrane attached to the hind legs and tail making a large wing. (per http://wolfdenpress.net/weasel.html )