Kinetic Monte Carlo (KMC) simulations are used to study transport of guest molecules in a two-phase medium in which the minority phase forms closed regions. This type of model system resembles compositions of mixed-matrix membranes (MMMs) made of a matrix and imbedded filler particles with different permeabilities. Based on an ideal filler-matrix composite morphology as defined in [H. Vinh-Thang, S. Kaliaguine, Chem. Rev. 113, 4980, 2013], the effects of the filler-particle volume fraction, particle size, shape (aspect ratio), and the spatial particle distribution on gas transport through MMMs are addressed. The results obtained for nonoverlapping and randomly placed spherical filler particles are found to be in good agreement with the analytical models available in the literature and have proven their good accuracy also for thin membranes where finite-size effects are expected to play an appreciable role. Furthermore, the prominent influence of the aspect ratio for nonspherical particles on the effective permeability is shown and scenarios are discussed where the alignment of the asymmetric filler particles give rise to anisotropic transport properties potentially favorable for the performance of MMMs. The KMC approach developed guides the optimal spatial arrangement and orientation of the filler particles for the different strategies to increase the membrane permeability and separation selectivity by transport enhancement or inhibition.