We give theoretical support to the splitting rule, which was recently observed numerically for the scattering from heterogeneous rough surfaces. Under certain general conditions, the incoherent intensity of a composite medium with a rough interface is the sum of the incoherent intensity of the rough homogeneous surface with an effective permittivity and the incoherent intensity of the same composite medium below a flat interface. The coherent intensity is merely that of the rough effective homogeneous surface. The effective permittivity is given accurately by the Bruggemann mixing rule, provided that the scale of fluctuations in the volume is small with respect to the electromagnetic wavelength.