Large Language Models (LLMs) remain highly vulnerable to jailbreak attacks, yet existing evaluations rely primarily on outcome-level metrics such as Attack Success Rate (ASR), providing limited insight into how and why safety failures occur. We propose an explanation-aware safety framework that augments binary harmfulness detection with structured, human-interpretable explanations capturing severity, strategies, trigger spans, rationales, and derived safety factors. To enable scalable and consistent supervision, we introduce a human--LLM hybrid annotation and canonicalization pipeline. We then fine-tune a compact model to generate canonical explanations alongside harmfulness decisions. Across both seen and unseen benchmark settings, our method improves robustness and explanation fidelity. In jailbreak defense evaluation, our approach reduces ASR to 0.44% on Vicuna-7B and 1.30% on GPT-3.5, outperforming existing defense baselines while also achieving the lowest StrongREJECT scores. Beyond outcome-level gains, the model more accurately recovers diagnostic attributes (e.g., attack strategy, trigger spans, and safety factors) than strong general-purpose LLM baselines. Overall, explanation-aware learning exposes diagnostic dimensions that ASR alone cannot capture and provides a more faithful and actionable foundation for robust LLM safety assessment.