Articulated object manipulation requires an understanding of kinematic structure that is difficult and costly to learn from robot demonstrations alone. We introduce the Kinematic-Aware Articulation Interface (KAI), a structured intermediate representation that captures the kinematic structure of articulated objects. By embedding interpretable geometric and kinematic priors into policy learning, KAI provides a strong inductive bias aligned with the underlying structure of articulated motion. This design effectively improves sample efficiency, with gains particularly pronounced in low-data regimes: across six simulation tasks, our method achieves an average success rate of 82.9%, matching or surpassing baseline performance while using only half the demonstration data. Our method also exhibits robust generalization to unseen backgrounds and visual distractors, transferring from a single clean training environment to cluttered real-world scenes. KAI's action-agnostic design further enables co-training with human interaction videos to enhance real-world robustness: under diverse visual distractions, our method with video co-training achieves over 70% average success rate.