Recent work on the mechanism of hole superconductivity is generalized to include interplanar hopping. The particular nature of the pairing interaction causes the superconducting state to remain isotropic, and the gap is constant over the three-dimensional Fermi surface. Nevertheless, significant anisotropy is found in the dependence of Tc on pressure, and comparison with recent pressure experiments is discussed. Other superconducting properties are found to be similar to those of the two-dimensional model and consistent with a variety of experimental results on oxides.