Adding mesopore networks in microporous materials using the principles of hierarchical structure design is recognized as a promising route for eliminating transport limitations and, therefore, for improving the value of the materials in technological applications. Depending on the routes of physico-chemical procedures or post-synthesis treatments used, very different geometries of the intentionally-added transport mesopores can be obtained. However, understanding the structure–dynamics relationships in these complex materials with multiple porosities under different thermodynamical conditions remains a challenging task. To address this problem, in this work, we provide a coarse-grained dynamic Monte Carlo modeling approach to study the transport properties of different hierarchical micro-mesoporous structures. Four common classes of bi-porous materials are considered, differing by the inter-connectivity of their mesoporous sub-spaces as one of the most important parameters determining the transport rates. The findings aid to correlate the messages of the various techniques of diffusion measurements.