In Parts I and II we developed a miscible-fingering macroscopic model for homogeneous media and showed how its formulation led to a consistent method for representing average fractional flows and pressure drops, including rectilinear problems where gravity causes either stabilizing or destabilizing influences on flow behavior. A key aspect was selection of a fingering function that allows fractional flow in the absence of gravity to match the empirical Koval model. We now extend this development to include problems in which heterogeneities create a stretching influence on the fractional-flow behavior, in a manner consistent with adoption of a Koval H-factor. The macroscopic model is extended to include a heterogeneous fingering function, and thence new results are derived for the heterogeneous average fractional flows and pressure drops, including again cases with positive and negative gravity contributions. The HRS-FD method described in Part I is used to obtain detailed fingering results for a class of ＇＇mildly heterogeneous＇＇ media, and thence the macroscopic model with its extended H-factor definition is shown to give accuracies at least as good as the previous homogenous cases. The corresponding Todd and Longstaff results with an appropriately adjusted omega are found to be less satisfactory for heterogeneous problems.