We develop a mechanistic model to represent the evolution of permeability in dual permeability dual stiffness sorbing media such as coal beds and shales. This model accommodates key competing processes of poromechanical dilation and sorption-induced swelling. Permeability evolution is cast in terms of series and parallel models with the series model better replicating observational data. The model may be cast in terms of nondimensional parameters representing sorptive and poromechanical effects and modulated by the sensitivity of the fracture network to dilation or compaction of the fractures. This latter parameter encapsulates the effects of fracture spacing and initial permeability and scales changes in permeability driven by either sorption or poromechanical effects. For a system following a Langmuir type sorption isotherm and where both poromechanical and swelling effects are individually large, a turnaround in net permeability from decreasing at low (sorbing) gas pressures to increasing at large gas pressures is expected. This new mechanistic model is capable of representing key aspects of these changes in the transport parameters of fractured sorbing media to changes in stress and pore pressure. This model is applied to well-controlled observational data for different ranks of coals, and different types of gases, and satisfactory agreement is obtained.