We investigate the multiscale geometrical and dimensional properties of fracture and fault networks crosscutting Lower Jurassic to Cretaceous shallow-water carbonate rocks. The carbonates are exposed along the flanks of the Viggiano Mt., on the eastern side of the High Agri Valley Basin of southern Italy. Furthermore, we employ the results of field and digital structural analyses to derive the input parameters for subsequent Discrete Fracture Network modelling (DFN) of geocellular volumes whose dimension and architecture resemble those of the investigated sites. DFN modelling is carried out for geocellular volumes representing the studied bed packages (5m-side volumes), outcrops (50m-side volumes), and reservoir-scale carbonate cliffs (500m-side volumes). Notably, modelling is obtained considering the minimum mechanical aperture value obtained in the field for porosity computations and theoretical values of fracture hydraulic aperture for permeability computations. This is because the mechanical aperture values and roughness profiles collected in the field along single fractures are unreliable due to weathering and localized karst-related dissolution. Our findings reveal that a scale-dependent geometry characterizes the Cretaceous carbonates over three orders of magnitude. These results support previously published data, and contrast with those obtained for the Lower Jurassic carbonates, which suffer of some bias due to the quality of the exposures. After DFN modelling, we show that the amount of computed fracture porosity is mainly due to the SB and NSB fractures, and that equivalent permeability is greater within faulted rock volumes. In terms of horizontal permeability, which is the most reliable result after DFN modelling, we document near isotropic horizontal permeability ellipses at all scales of observations. At individual outcrops, we note that the permeability ellipses are elongated parallel to the dominant fault sets that denotes how localized strain affects the directionality of fluid flow. Finally, we summarize the original data in a conceptual model illustrating the modalities of meteoric fluid infiltration through the vadose zone, and then subsequent horizontal flow in the phreatic zone present within the fracture carbonates at shallow depths.