We documented the porosity, permeability, pore geometry, pore type, textural anisotropy, and capillary pressure of carbonate rock samples collected along basin‐bounding normal faults in central Italy. The study samples consist of one Mesozoic platform carbonate host rock with low porosity and permeability, four fractured host rocks of the damage zones, and four fault rocks of the fault cores. The four fractured samples have high secondary porosity, due to elongated, connected, soft pores that provide fluid pathways in the damage zone. We modeled this zone as an elastic cracked medium, and used the Budiansky–O'Connell correlation to compute its permeability from the measured elastic moduli. This correlation can be applied only to fractured rocks with large secondary porosity and high‐aspect ratio pores. The four fault rock samples are made up of survivor clasts embedded in fine carbonate matrices and cements with sub‐spherical, stiff pores. The low porosity and permeability of these rocks, and their high values of capillary pressure, are consistent with the fault core sealing as much as 77 and 140 m of gas and oil columns, respectively. We modeled the fault core as a granular medium, and used the Kozeny–Carmen correlation, assigning the value of 5 to the Kozeny constant, to compute its permeability from the measured porosities and pore radii. The permeability structure of the normal faults is composed of two main units with unique hydraulic characteristics: a granular fault core that acts as a seal to cross‐fault fluid flow, and an elastic cracked damage zone that surrounds the core and forms a conduit for fluid flow. Transient pathways for along‐fault fluid flow may form in the fault core during seismic faulting due to the formation of opening‐mode fractures within the cemented fault rocks.