We extend the periodic charge-dipole electrostatic model, see I. V. Bodrenko, M. Sierka, E. Fabiano, and F. Della Sala, J. Chem. Phys. 137, 134702 (2012), to include a kinetic-exchange-correlation (KXC) correction. The KXC correction is approximated by means of an extended-Hückel-type formula, it is exact in the infinite jellium model and it is also computationally efficient as it requires only the computation of overlap integrals. Tests on the linear response of silver slabs to an external electrostatic perturbation show that the KXC correction yields a very accurate description of induced dipole and of the whole induced charge density profile. We also show that the KXC parameters are quite transferable and related to the atomic polarizability.