Mixed-matrix membranes (MMMs) consisting of an ortho-hydroxy polyamide (HPA) matrix, and variable loads of a porous polymer network (PPN) were thermally treated to induce the transformation of HPA to polybenzoxazole (β-TR-PBO). Two different HPAs were synthesized to be used as a matrix, 6FCl-APAF and tBTpCl-APAF, while the PPN used as a filler was prepared by reacting triptycene and trifluoroacetophenone. The permeability of He, H2, N2, O2, CH4 and CO2 gases through these MMMs are analyzed as a function of the fraction of free volume (FFV) of the membrane and the kinetic diameter of the gas, allowing for the evaluation of the free volume. Thermal rearrangement entails an increase in the FFV. Both before and after thermal rearrangement, the free volume increases with the PPN content very similarly for both polymeric matrices. It is shown that there is a portion of free volume that is inaccessible to permeation (occluded volume), probably due to it being trapped within the filler. In fact, permeability and selectivity change below what could be expected according to densities, when the fraction of occluded volume increases. A higher filler load increases the percentage of inaccessible or trapped free volume, probably due to the increasing agglomeration of the filler. On the other hand, the phenomenon is slightly affected by thermal rearrangement. The fraction of trapped free volume seems to be lower for membranes in which the tBTpCl-APAF is used as a matrix than for those with a 6FCl-APAF matrix, possibly because tBTpCl-APAF could approach the PPN better. The application of an effective medium theory for permeability allowed us to extrapolate for a 100% filler, giving the same value for both thermally rearranged and non-rearranged MMMs. The pure filler could also be extrapolated by assuming the same tendency as in the Robeson’s plots for MMMs with low filler content.