Despite numerous observational and theoretical attempts, the heating problem of the solar chromosphere still remains unsolved. We develop a novel 3D two-fluid model that accounts for dynamics of charged species and neutrals, and use it to perform the numerical simulations of granulation driven jets and associated waves in a quiet region of the solar chromosphere. The energy carried by the waves is dissipated through ion-neutral collisions, which are sufficient to balance radiative energy losses and to sustain the quasi-stationary atmosphere whose ion and neutral number densities, ionization fraction, and temperature profiles are relatively close to the observationally based semi-empirical model. Additional verification of our results is provided by a good fit of the numerically predicted waveperiod variations with height to the recent observational data. These observational validations of the numerical results demonstrate that the wave heating problem of a quiet region of the chromosphere may be solved.