Thematic analysis (TA) is a widely used qualitative approach for uncovering latent meanings in unstructured text data. TA provides valuable insights in healthcare but is resource-intensive. Large Language Models (LLMs) have been introduced to perform TA, yet their applications in healthcare remain unexplored. Here, we propose TAMA: A Human-AI Collaborative Thematic Analysis framework using Multi-Agent LLMs for clinical interviews. We leverage the scalability and coherence of multi-agent systems through structured conversations between agents and coordinate the expertise of cardiac experts in TA. Using interview transcripts from parents of children with Anomalous Aortic Origin of a Coronary Artery (AAOCA), a rare congenital heart disease, we demonstrate that TAMA outperforms existing LLM-assisted TA approaches, achieving higher thematic hit rate, coverage, and distinctiveness. TAMA demonstrates strong potential for automated TA in clinical settings by leveraging multi-agent LLM systems with human-in-the-loop integration by enhancing quality while significantly reducing manual workload.