Concerning their permeability how are membranes classified?

Membranes can be divided as impermeable, permeable, semipermeable or selectively permeable.

An impermeable membrane is that by which no substance can pass. Semipermeable membranes are those that let only solvents, like water, to pass by it. Permeable membranes are those that let solvent and solutes, like ions and molecules, to pass across it. There are also selectively permeable membranes, i.e., membranes that besides permitting the passage of solvent let only some specific solutes to pass while blocking others.