A system of quasi-hydrodynamic equations for the electric field, charges, and concentrations of cloud particles and light aeroions in stratified regions of mesoscale convective systems is proposed and analyzed numerically in a one-dimensional approximation. The important role of Debye-charge layers, which are caused by light ions, is established. It is shown that, under certain aerodynamic conditions, both noninductive and inductive melting-related charging of particles may cause a narrow intense positive-charge layer to form near the zero-temperature isotherm; the altitude at which the vertical velocity component changes sign with respect to the height of the zero-temperature isotherm is of particular importance. When consideration is taken for an inductive charging mechanism and the real structure of the rising flow’s velocity, the distributions of charges and field strength (with a peak of about 100 kV/m), which describe the profiles observed in experiments, form in about 30 min. Taking into account the polarization of melting aggregates and water drops in an electric field when aeroions attach to them causes the rate of generating electric-charge layers to reduce. Thus, the solutions obtained in this study describe the structure and dynamics of spatially separated regions of electric charges in the stratified region and offer a satisfactory explanation for the experimental data. The results are important for explaining the abnormally high lightning activity of mesoscale convective systems, their role in initiating charges in the middle atmosphere, and maintaining the quasi-stationary state of the global electric circuit.