Emotional support (ES) systems alleviate users' mental distress by generating strategic supportive dialogues based on diverse user situations. However, ES systems are limited in their ability to generate effective ES dialogues that include timely context and interpretability, hindering them from earning public trust. Driven by cognitive models, we propose Mind-to-Mind (Mind2), an ES framework that approaches interpretable ES context modeling for the ES dialogue generation task from a discourse analysis perspective. Specifically, we perform cognitive discourse analysis on ES dialogues according to our dynamic discourse context propagation window, which accommodates evolving context as the conversation between the ES system and user progresses. To enhance interpretability, Mind2 prioritizes details that reflect each speaker's belief about the other speaker with bidirectionality, integrating Theory-of-Mind, physiological expected utility, and cognitive rationality to extract cognitive knowledge from ES conversations. Experimental results support that Mind2 achieves competitive performance versus state-of-the-art ES systems while trained with only 10\% of the available training data.