This article proposes a two-level distributed energy scheduling framework for the coordinated operation of regional integrated energy systems (RIESs), and investigates its effects on the optimal operation of multiarea energy systems (MAESs). The MAES includes an integrated energy distribution system (IEDS) and several networked-RIESs. The IEDS is defined as an integrated system of electrical and natural gas networks. Moreover, the RIES is assumed as a system of multiple local energy carriers such as electricity, heat, and natural gas to provide energy demands. In this research, the IEDS and each RIES are considered as independent systems with individual objectives, so that multiple energy carriers can be directly traded between RIESs. In order to solve the coordinated optimization problems of these interconnected subsystems, the current study implements a distributed optimization framework based on the analytical target cascading structure. In this manner, this study employs an Augmented Lagrangian based penalty function. To solve the local optimization problem of individual energy systems, we utilize the teaching–learning based optimization algorithm. The performance of the proposed method is validated on a test MAES including an IEDS, and three RIESs.