Simulation analysis is critical for identifying possible hazards and ensuring secure operation of power systems. In practice, large-disturbance rotor angle stability and voltage stability are two frequently intertwined stability problems. Accurately identifying the dominant instability mode (DIM) between them is important for directing power system emergency control action formulation. However, DIM identification has always relied on human expertise. This article proposes an intelligent DIM identification framework that can discriminate among stable status, rotor angle instability, and voltage instability based on active deep learning (ADL). To reduce human expert efforts required to label the DIM dataset when building DL models, a two-stage batch-mode integrated ADL query strategy (preselection and clustering) is designed for the framework. It samples only the most helpful samples to label in each iteration and considers both information contents and diversity in them to improve query efficiency, significantly reducing the required number of labeled samples. Case studies conducted on a benchmark power system (China Electric Power Research Institute (CEPRI) 36-bus system) and a practical large-area power system (Northeast China Power System) reveal that the proposed approach outperforms conventional methods in terms of accuracy, label efficiency, scalability, and adaptability to operational variability.