An extension of the MMM2D method, called ICMMM2D, is presented to deal with the electrostatic interactions in partially periodic systems that are confined along one direction by two planar dielectric interfaces. The method handles all electrostatic interactions that are induced by the presence of dielectric interfaces by an image charge method. Our method accurately treats repeated image charges under the planar dielectric interfaces as well as the periodic images that are due to the periodic boundary conditions along the other two directions. The scaling of the method with the number of charges, N, is still N5/3, and the overhead involved approximately doubles the CPU time compared to the original MMM2D method. The errors are fully under control and the error bounds can be preset up to computer accuracy.