The electronic and electromechanical properties of complex oxide superlattices are closely linked to the evolution of the structure and electrical polarization of the component layers in applied electric fields. Efforts to deduce the responses of the individual components of the superlattice to applied fields have focused on theoretical approaches because of the limitations of available experimental techniques. Time-resolved x-ray microdiffraction provides a precise crystallographic probe of each component using the shift in wave vector and change in intensity of superlattice satellite reflections. We report in detail the methods to measure and analyze the x-ray diffraction patterns in applied electric field and their application to a 2-unit-cell BaTiO3/4-unit-cell CaTiO3 superlattice. We find that the overall piezoelectric distortion is shared between the two components. Theoretical predictions of the electromechanical properties of a superlattice with the same composition constrained to tetragonal symmetry are in excellent agreement with the experiments. Lattice instability analysis, however, suggests that the low-temperature ground state could exhibit antiferrodistortive rotations of TiO6 octahedra within and/or at the interfaces of the CaTiO3 component.