We calculate the short-range contributions C(1) and C(10) to the angular intensity correlation function for the scattering of s-polarized light from a one-dimensional random interface between two dielectric media. The calculations are carried out on the basis of a new approach that separates out explicitly the contributions C(1) and C(10) to the angular intensity correlation function. The contribution C(1) displays peaks associated with the memory effect and the reciprocal memory effect. In the case of a dielectric-dielectric interface, which does not support surface electromagnetic surface waves, these peaks arise from the coherent interference of multiply-scattered lateral waves supported by the interface. The contribution C(10) is a structureless function of its arguments.