The interest in the role of the solar wind termination shock (TS) and heliosheath in cosmic ray modulation studies has increased significantly as the Voyager 1 and 2 spacecraft approach the estimated position of the TS. For this work the modulation of cosmic ray protons (p) and antiprotons ($bar{rm p}$), and the consequent charge-sign dependence, is studied with a numerical model including a TS with diffusive shock acceleration, a heliosheath, and drifts. The model allows a comparison of modulation with and without a TS. A more fundamental and comprehensive set of diffusion coefficients is used, applicable to a number of cosmic ray species during both magnetic polarity cycles of the Sun. Newly computed and improved local interstellar spectra for p and $bar{rm p}$ are used. The modulation of p with an anomalous component is also done to establish charge-sign dependence at low energies. The modulation effects of the heliosheath and TS are illustrated for the different species and how they affect the computed $bar{rm p}$/p. We found that the computed modulation for $bar{rm p}$ is surprisingly different from p and that the heliosheath is important for cosmic ray modulation. The local proton interstellar spectrum may not be known at energies <~1 GeV until a spacecraft actually approaches the heliopause because of the strong modulation that occurs in the heliosheath, the effect of the TS, and the presence of anomalous protons. For antiprotons, in contrast, these effects are less pronounced.