This article presents an extension of the recently introduced planewave density interpolation method to the electric-field integral equation (EFIE) for problems of scattering and radiation by perfect electric conducting objects. Relying on the Kirchhoff integral formula and local interpolations of the surface currents that regularize the kernel singularities, the technique enables off- and on-surface EFIE operators to be reexpressed in terms of integrands that are globally bounded (or even more regular) over the domain of integration, regardless of the magnitude of the distance between the target and source points. Surface integrals resulting from the application of the method of moments using the Rao-Wilton-Glisson basis functions can then be directly evaluated by means of elementary quadrature rules irrespective of the singularity location. The proposed technique can be applied to simple and composite surfaces comprising two or more overlapping components. The use of composite surfaces can significantly simplify the geometric treatment of complex structures, as the density interpolation method enables the use of separate nonconformal meshes for the discretization of each of the surface components that make up the composite surface. A variety of examples, including multiscale and intricate structures, demonstrate the effectiveness of the proposed methodology.