The rise of large language models (LLMs) has enabled us to seek answers to inherently debatable questions on LLM chatbots, necessitating a reliable way to evaluate their ability. However, traditional QA benchmarks assume fixed answers are inadequate for this purpose. To address this, we introduce DebateQA, a dataset of 2,941 debatable questions, each accompanied by multiple human-annotated partial answers that capture a variety of perspectives. We develop two metrics: Perspective Diversity, which evaluates the comprehensiveness of perspectives, and Dispute Awareness, which assesses if the LLM acknowledges the question's debatable nature. Experiments demonstrate that both metrics align with human preferences and are stable across different underlying models. Using DebateQA with two metrics, we assess 12 popular LLMs and retrieval-augmented generation methods. Our findings reveal that while LLMs generally excel at recognizing debatable issues, their ability to provide comprehensive answers encompassing diverse perspectives varies considerably.