A mesoscopic rheological model of suspensions of semiflexible fibers in polymeric fluids is formulated. Consequences of the model are compared with results of experimental observations of the rheological properties in a simple shear flow. The model takes into account the fiber-fiber and fiber-polymer interactions (in the free energy and the mobility coefficients) and the semiflexible nature of the fibers (in the choice of the Khokhlov-Semenov entropy).