An improved Monte-Carlo model of ionic transport across a solid interface in two-dimensional triangular lattice is presented. The new features of the model are: (i) more-realistic form of the microscopic potential of the ion-ion interaction, and (ii) accounting of the mutual ion interactions up to second nearest neighbors. This way it is possible to simulate more flexible the ionic transport across the real interface between a fast-ion conducting glass and the intercalate in the cathode of a Lithium thin-film battery. Numerical results computed with this model are presented by emphasizing on the influence of the internal interface on the ion distribution, the site energies and the open circuit voltage. (author). 15 refs, 5 figs.