It is common practice to define reflexion and transmission coefficients for waves propagating through isotropic and anisotropic inhomogeneous plasma in terms of coefficients of waves existing within homogeneous regions of the plasma below and above the inhomogeneity. This concept is shown to be very restricted, and corresponding coefficients are defined for solutions existing within the inhomogeneous regions of the plasma. The extended concept is shown to satisfy conditions usually associated with the more common definitions, notably energy conservation and reciprocity. The theory is developed using integral equations and matrix theory, and special precautions are taken so that the results extend from the inhomogeneous plasma into free-space domains.