Using high-resolution inelastic neutron scattering measurements of the density of states of ice, we observed two well-separated molecular optic bands at 27 and 37 meV for ice I. Our lattice dynamic model has demonstrated that in order to reproduce the phonon density of states, two different interaction strengths among the H-bonds in ice I associated with the proton disorder have to be assumed. Such large differences in the force constants of two types of H-bonds randomly distributed in the network of ice, having a strength ratio of almost 1 : 2, could be attributed to dipole or other types of electronic interactions. Support for this hypothesis is provided by a series of measurements on different ice structures. The implications of this model are considerable. It is capable of explaining not only many properties of ices, but also, without further hypothesis, a wide range of anomalous properties of water, such as the specific heat, supercooling, density and entropy fluctuations, etc. The applications of the model are discussed.