The dipolar susceptibility of interfacial water and the corresponding interface dielectric constant were calculated from numerical molecular dynamics simulations for neutral and charged states of buckminsterfullerene C-60. Dielectric constants in the range 10-22, depending on temperature and solute charge, were found. These values are consistent with recent reports for biological and nanometer-scale interfaces. The hydration water undergoes a structural crossover as a function of the surface charge of the charged fullerene. Its main signatures include the release of dangling O-H bonds pointing toward the solute and the change in the preferential orientations of hydration water from those characterizing hydrophobic to charged substrates. The interface dielectric constant marks the structural transition with a spike showing a Curie-type phenomenology. The computational formalism adopted here provides direct access to interface susceptibility from configurations produced by computer simulations. The required property is the cross-correlation between the radial projection of the dipole moment of the solvation shell with the electrostatic potential of the solvent inside the solute.