The possibility to electrically tune the optical transparency of thin membranes is of significant interest for a number of possible applications, such as controllable light diffusers and smart windows, both for residential and mobile use. As a difference from state-of-the-art approaches, where with an applied voltage the transparency can only increase or decrease, this paper presents the first concept to make it electrically tuneable to both higher and lower values, within the same device. The concept is applicable to any soft insulating membrane, by coating both of its surfaces with a circular transparent stretchable conductor, surrounded by a stretchable annular conductor. The two conductors are used as independently addressable electrodes to generate a dielectric elastomer-based actuation of the membrane, so as to electrically control its surface topography. We show that the optical transmittance can electrically be modulated within a broad range, between 25% and 83%. This approach could be especially advantageous for systems that require such a broad tuning range within structures that have to be thin, lightweight and acoustically silent in operation.