In several Lidar techniques molecular backscattering from atmospheric gases is considered, e.g. Raman lidar technique, and elastic molecular scattering by HSR1 technique are employed. When larger particles are also present in the sounded zone, Mie scattering contributions are superposed to the Lidar molecular signal. Because the efficiency of the Mie scattering is very high with respect to the molecular one, the effect of Mie scattering can be very strong for typical tropospheric clouds or aerosol structures, when multiple scattering contribution becomes important. In this case the incident, or the molecular scattered radiation, can be multiply scattered from the aerosols. There is no significant multiple molecular scattering, but larger particle scattering processes occur in addition to one molecular scattering. A Monte Carlo code developed for studying this effect is described by means of a flow diagram showing the details of the procedure. The code allows the consideration of depolarization for the molecular return due to the intervening effect of Mie scattering. Some results in some cases of realistic models of atmospheric structures are presented, showing increase of the molecular returns by factors even of the order of a few units. Comparisons with published data by other authors will be shown.