We generalize a recently developed polymer density functional theory (PDFT) for polydisperse polymer fluids to the case of semiflexible (stiff) polymers. As with our earlier work on flexible polymers, we show here that the generalization of the PDFT to polydisperse: mixtures of semiflexible chains allows us to obtain a remarkable simplification of the solution algorithm, compared to the monodispersed case. The number of required equations for complete solution of the (polydisperse) PDFT scales inveresly with the width of the polydispersity profile. This reflects the fact that more information is required, the narrower is the polydispersity. We apply the theory to a number of model scenarios, including repulsive and adsorbing surfaces. We find that polydispersity effects on the depletion interaction are larger for dilute solutions and when the Surfaces arc adsorbing. We also investigate short, stiff chains and find rather dramatic effects in the presence of adsorbing surfaces.