A self-consistent method of characterizing vertical turbulent transport by means of a diffusion parameter is demonstrated for the extremely inhomogeneous case of layered turbulence in a stratified fluid. Between the horizontal turbulent layers, horizontal laminar flow is assumed to occur, and molecular diffusion is ignored. The layers are assumed to occur at random heights with random thickness. An analogy is made between the process of random mixing layers and the finite difference representation of the diffusion equation. It is demonstrated by means of a series of digital computer experiments that, in the case where total mixing takes place within the turbulent layers, the diffusion parameter herein developed is the valid one to use (in contrast to 'eddy diffusivity'). The relation between this inhomogeneous diffusion parameter and practical experimental measurements is given. The motive behind this investigation involves vertical transport of pollution in the environment in general and in the stratosphere in particular.