A composite glass pane that contains two glass panes or two polymer panes or one glass pane and one polymer pane and has at least one polymer film bonded therebetween, wherein a first type of polymer film having a first stiffness is arranged in a first, larger areal region of the composite glass pane and a second type of polymer film having a second, higher stiffness than the first polymer film is arranged in at least one second areal region.