A three-dimensional Fourier expansion has been developed to describe the dispersion relations $E(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}})$ for the $\ensuremath{\pi}$ bands of graphite throughout the Brillouin zone. The coefficients of the Fourier expansion are evaluated by a fit to the experimentally determined parameters of the Slonczewski-Weiss model, as well as to the optical data. Using this energy-band model, the interband contribution to the frequency-dependent dielectric constant has been calculated in the energy range $0.5l\ensuremath{\hbar}\ensuremath{\omega}l6$ eV for both $\stackrel{\ensuremath{\rightarrow}}{\mathrm{E}}\ensuremath{\perp}\stackrel{\ensuremath{\rightarrow}}{\mathrm{c}}$ and $\stackrel{\ensuremath{\rightarrow}}{\mathrm{E}}\ensuremath{\parallel}\stackrel{\ensuremath{\rightarrow}}{\mathrm{c}}$. For this calculation, a numerical-integration procedure has been developed to carry out the full-zone integrations. The results for the dielectric constant are primarily dependent on the values of the McClure parameters ${\ensuremath{\gamma}}_{0}$, ${\ensuremath{\gamma}}_{1}$, ${\ensuremath{\gamma}}_{3}$, and ${\ensuremath{\gamma}}_{4}$, which enter the Slonczewski-Weiss Hamiltonian for graphite.