In this paper, pragmatic and robust techniques have been developed to simultaneously interpret absolute permeability and relative permeability together with capillary pressure in a naturally fractured carbonate formation from wireline formation testing (WFT) measurements. By using two sets of pressure and flow rate field data collected by a dual-packer tool, two high-resolution cylindrical near-wellbore numerical models are developed for each dataset on the basis of single- and dual-porosity concepts. Then, simulations and history matchings are performed for both the measured pressure drawdown and buildup profiles, while absolute permeability is determined and relative permeability is interpreted with and without considering capillary pressure. Compared to the experimentally measured relative permeability curves for the same formation collected from the literature, relative permeability interpreted with consideration of capillary pressure has a better match than those without considering capillary pressure. Also, relative permeability obtained from dual-porosity models has similar characteristics to those from single-porosity models especially in the region away from the endpoints, though the computational expenses with dual-porosity models are much larger. Absolute permeabilities in the vertical and the horizontal directions of the upper layer are determined to be 201.0 mD and 86.4 mD, respectively, while those of the lower layer are found to be 342.9 mD and 1.8 mD, respectively. Such a large vertical permeability of the lower layer reflects the contribution of the extensively distributed natural fractures in the vertical direction.