A recently reported nonlinear model of the bending of a thin-film/substrate bilayer provides a means for determining stress in thin films even for large deflection and ellipsoidal bending. This model replaces the usual Stoney's equation, which is valid only for small deflections. However, the model omits consideration of the commonly observed initial curvature of the substrate before deposition. In the small deflection regime the principle of superposition justifies simply subtracting the initial curvature from the final curvature after deposition, but for large deflections this is inappropriate, because the principle of superposition is no longer valid. The present paper presents a modified form of the nonlinear model incorporating initial substrate bending. The resulting equations show that initial substrate curvature causes magnified nonlinear effects and provide a means for determining film and substrate elastic properties in addition to thin-film stress.