We determined the anisotropic dielectric response of graphite by means of time-dependent density-functional theory and high-resolution valence electron energy-loss spectroscopy. The calculated loss function was in very good agreement with the experiment for a wide range of momentum-transfer orientations with respect to the graphitic basal planes, provided that local-field effects were included in the response. The calculations also showed strong effects of the interlayer Coulomb interaction on the total pi+sigma plasmon. This finding must be taken into account for the explanation of recent loss spectra of carbon nanotube materials.