Subjecting a liquid/liquid interface to an electrohydrodynamic pressure enhances fluctuations with a characteristic wavelength leading to an instability and the formation of well-defined columnar structures. An extension of a linear stability analysis for a single fluid interface to the bilayer case produced general arguments applicable to any interface. Countering the electrohydrodynamic pressure is the Laplace pressure, which for films is dictated by the surface energy; whereas for a bilayer, it is given in terms of the interfacial energy. Consequently, the characteristic length scale is reduced in the case of bilayers. Results are presented for different polymer bilayers under a wide range of experimental conditions showing quantitative agreement with the generalized theory with no adjustable parameters. Over 4 orders of magnitude in reduced wavelength and field strength can be described by these arguments. These results point to a viable route by which structures can be produced over a wide range of length scales.