Diffusion coefficient of a particle diffusing near the interface of two immiscible liquids varies when the particle crosses the interface. We show how the problem of lateral diffusion in such a system can be reduced to that of finding the distribution of the cumulative residence time spent by the particle in one of the layers. The latter problem can be solved with relative ease since the distribution is determined by the one-dimensional motion in the direction normal to the interface. The approach is utilized to find an exact solution for the Fourier--Laplace transform of the lateral propagator, the effective medium approximation for this propagator, and the time-dependent behavior of the lateral diffusion coefficient in several special cases.

PACS numbers: 82.20.Fd, 05.40.--a