With the increasing interconnection between gas and power networks, a small fraction of failed components caused by extreme events may trigger widespread cascading failures in an interdependent gas and power network (IGPN). A question of practical interest is how many initially failed components could break down the whole network, which can help us determine the condition for the collapse of the system. Considering that, the resilient region defined by the expected minimal fraction of initially failed components to break down the system is proposed for IGPNs to analyze the system resilience from a macroscopic perspective. To determine the resilient region, an innovative model is proposed based on the combination of percolation theory (that has been widely used in complex science) and statistical physics methods. Specifically, initial stochastic disturbances are simulated by a percolation model which progressively removes failed components from the network, and the percolation threshold (i.e., a critical fraction of failed components breaking down the network) is used as a statistical indicator for the system collapse conditions. On this basis, the boundaries of resilient regions can be characterized by the curves of the percolation threshold, and the corresponding resilience indices are developed. Considering the realistic failure propagation behaviors triggered by initial disturbances, a flow heterogeneity-driven cascading failure (FHCF) model is proposed, by which the resilient region can be computed numerically. Besides, criticality metrics are proposed to evaluate the influence of each component on the resilient region. Finally, the effectiveness of the approach is demonstrated on two test IGPNs, and measures to enhance the resilience of IPGNs are concluded.