The traditional diffuse mismatch model allows only elastic scattering processes and therefore underpredicts the thermal boundary conductance between two acoustically mismatched solids. To fix it, models that take inelastic scattering into consideration have been proposed. However, many of them do not take the contribution of the temperature derivative of the transmissivity into consideration; some allow phonons that are reflected by the interface in lower-level anharmonic phonon processes to further participate in higher-level ones, resulting in high transmissivity at elevated temperature. In this work, modifications are proposed to fix the above two drawbacks. Necessary physical assumptions are made clearly to distinguish the total energy flux and the participating energy flux associated with each level of processes. Agreement of the predictions with the experimental measurements is obtained by adjusting the ratio of these two fluxes.