Electric-field-induced interfacial instabilities of a dielectric elastic membrane confined between a pair of leaky dielectric liquid layers are investigated by linear stability analysis. The role of leaky surroundings is investigated by comparing the instability modes in three different systems: (a) purely dielectric surrounding layers, (b) one leaky and the other pure dielectric layer, and (c) leaky dielectric surrounding layers. The interfaces of the trilayer can become unstable either by a long-wave in-phase bending mode or by a finite-wavenumber antiphase squeezing mode. In all the cases, the conditions for the transition from the finite-wavenumber to long-wave mode are compared and contrasted. The study uncovers that the charge leakage in the surrounding layers of the elastic film not only changes the amplitude of deformations at the interfaces but also causes a transition of dominant modes from bending to squeezing. In addition to the presence of the induced dipoles, the augmented destabilizing influence at the interfaces(s) due to free charges from the charge leakage inside the films is found to significantly reduce the length scale. The same effect also reduces the requirement for the minimum field intensity to engender the electro-hydrodynamic (EHD) instabilities in the elastic films. Thus, the study is also relevant in improving the understanding of the fundamental aspects of the electric field induced deformation and rupture of biological membranes in the electrolytes.