The enhanced backscattering of light from randomly rough metal surfaces, which manifests itself as a well-defined peak in the retroreflection direction in the angular distribution of the intensity of the light scattered incoherently has attracted a great deal of attention recently. The backscattering phenomenon is attributed to the coherent interference of multiply-scattered surface plasmon polaritons excited on a metal surface with their time-reversed partners. The coherent interference of multiply-scattered lateral waves excited in the scattering of light from strongly rough dielectric surfaces is known to lead to an enhanced backscattering peak in the angular distribution of the intensity of s-polarized light scattered from them. In this paper we present an analytical theory of the scattering of light from a one- dimensional randomly rough interface between two media. One of the media is a dipole-active medium that is characterized by a frequency-dependent dielectric function, that is negative in a restricted frequency range, while the other is characterized by a frequency-independent, real, positive dielectric constant. We assume that the interface profile function is a single-valued function of the coordinate in the mean plate of the interface that is normal to its grooves and ridges, and constitutes a zero-mean, stationary, Gaussian random process. We assume that either p- or s-polarized electromagnetic waves are incident on the interface from the medium whose dielectric constant is frequency-independent. We study the angular distribution of the light that has been scattered incoherently as a function of the frequency of the incident light. The evolution of the enhanced backscattering peak in the case of p-polarized incident light as the frequency of the incident light is tuned through the frequencies of the dipole-active excitations in the medium whose dielectric function is frequency-dependent, is studied. Different mechanisms for the formation of the enhanced backscattering peak in different frequency regions are discussed.