For the behavior analysis of cooperative-antagonistic networks (CANs), the structural balance theory has been adopted widely since it can be developed to accommodate the simultaneous existence of competitive interactions. This advantage of structural balance is further explored in this paper by aiming at the local nodes instead of the global CAN, and a notion of structurally balanced nodes is proposed. It is shown that structurally balanced nodes play a dominant role in determining the dynamic behaviors of CANs. Furthermore, such an extension of structural balance is applied to distinguish the roles of all nodes to create a hierarchical structure decomposition of CANs. Particularly, regarding interval bipartite consensus of quasi-strongly connected CANs, the impact index of root nodes can be calculated directly through counting the number of structurally balanced nodes.