Threatened by natural disasters and man-made attacks, the resilient operation of power systems has drawn increased attention, which gives rise to a greater demand for power generation assets with high operational flexibility, such as natural gas power plants (NGPPs). This, in turn, results in a greater proportion of NGPPs and greater interdependence between power and gas systems. As a consequence, the modeling of the interactions between power systems and natural gas systems to achieve operational resilience in power systems becomes extremely vital. This topic has been discussed by quite a few researchers; however, previous studies suffered from two major drawbacks, namely (1) they assumed the existence of only one utility that has full control authority over the power system and gas system; (2) the economic interactions between power systems and gas systems have been neglected, which goes against current industrial practice. In this study, the power system and gas system are regarded as two individual utilities and their physical and economic interactions are modeled by considering the fuel consumption of the NGPPs and gas contracts and by guaranteeing the fuel availability of NGPPs in the pre- and post-contingency stages, respectively. The proposed model is developed based on a two-stage robust decision-making framework to optimize the operational performances of power systems under the worst-case N-k contingencies. To deal with the binary variables introduced by the linearization of the Weymouth equation and the on/off grid operation of generators, the nested column-and-constraint generation (NC&CG) algorithm is adopted. The necessity of considering economic and physical interactions between power systems and natural gas systems and the effectiveness of the proposed model and algorithm are verified by numerical simulations of two test systems.