Self-assembly in the presence of external forces is an adaptive, directed organization of molecular components under nonequilibrium conditions. While forces may be generated as a result of spontaneous interactions among components of a system, intervention with external forces can significantly alter the final outcome of self-assembly. Superimposing these intrinsic and extrinsic forces provides greater degrees of freedom to control the structure and function of self-assembling materials. In this work we investigate the role of electric fields during the dynamic self-assembly of a negatively charged polyelectrolyte and a positively charged peptide amphiphile in water leading to the formation of an ordered membrane. In the absence of electric fields, contact between the two solutions of oppositely charged molecules triggers the growth of closed membranes with vertically oriented fibrils that encapsulate the polyelectrolyte solution. This process of self-assembly is intrinsically driven by excess osmotic pressure of counterions and the electric field is found to modify the kinetics of membrane formation as well as membrane morphology and properties. Depending on the strength and orientation of the field we observe a significant increase or decrease of up to nearly 100% in membrane thickness, or the controlled rotation of nanofiber growth direction by 90 degrees which leads to a significant increase in mechanical stiffness. These results suggest the possibility of using electric fields to control structure in self-assembly processes that involve the diffusion of oppositely charged molecules.