We find experimentally that the optical sheet conductance of graphite per graphene layer is very close to (π/2)e2/h, which is the theoretically expected value of dynamical conductance of isolated monolayer graphene. Our calculations within the Slonczewski-Weiss-McClure model explain well why the interplane hopping leaves the conductance of graphene sheets in graphite almost unchanged for photon energies between 0.1 and 0.6 eV, even though it significantly affects the band structure on the same energy scale. The f-sum rule analysis shows that the large increase of the Drude spectral weight as a function of temperature is at the expense of the removed low-energy optical spectral weight of transitions between hole and electron bands.