The in-plane anisotropy (epsilon(x) not equal epsilon(y)) and the off-plane anisotropy (epsilon(x) not equal epsilon(z)) of ZnSe/GaAs interfaces formed under conditions that promote the formation of either Zn-As or Ga-Se bonds are studied by reflectance difference spectroscopy. Two resonance Lines, one at 2.70 eV and the other around 3.0 eV, have been observed. The in-plane anisotropy is along the [110] and the [<1(1)under bar0>] principal axes. The dependence of the resonances on interface formation conditions, the results of the photoreflectance spectroscopy, and the annealing experiments all suggest that the anisotropy is not due to the electro-optic effect resulting from an interface electric field. The reflectance difference spectroscopy results are consistent with the assumption that the anisotropy is the intrinsic properties of ordered ZnSe/GaAs heterovalent interface, that the resonance at 2.70 eV is associated with the interface state of Zn-As bonds and the resonance near 3.0 eV is associated with the interface state of Ga-Se bonds. The presence of a thin layer of S at the ZnSe/GaAs interfaces results in a third resonance at 3.2 eV, probably due to the Ga-S bends. The resonance line shape changes as the top layer thickness varies. Such change can be well explained by a three-layer system with the conventional Fresnel optics and is understood as due to the ZnSe top layer. It is our hope that our results will stimulate more interest in the theoretical study of this interface.