High-strength droplet interfaces are attractive for many applications, specifically in cases where droplets are channeled through fluidic devices and manipulated by electromagnetic fields. Using models and experiments, we study the deformation of droplets and capsules with protein interfaces in an electric field in thin and wide electrode gaps. Proteins are chosen from candidates expected to display qualitatively different interfacial interactions and strengths: a globular protein (bovine serum albumin), a reversible cross-linking peptide (AFD4), and a hydrophobin (cerato ulmin). Dilute protein additives can lead to over 1 order of magnitude stronger oil-water interfaces than those stabilized by small surfactants. We develop small deformation models to evaluate a protein membrane's interfacial elasticity, notably accounting for the electric field perturbation encountered in a gap and a careful treatment of a generalized elastic interface with both surface tension and interfacial elasticity. Results indicate that globular proteins, which typically have comparable surface tension and interfacial elasticity, can be modeled well by this generalized elastic interface. We further find that when in a gap, droplets and capsules migrate toward one electrode, deform asymmetrically, exhibit polar spreading on the electrode, and predictably stretch more than in the infinite gap scenario at constant field strength.