Obtaining stakeholders' diverse experiences and opinions about current policy in a timely manner is crucial for policymakers to identify strengths and gaps in resource allocation, thereby supporting effective policy design and implementation. However, manually coding even moderately sized interview texts or open-ended survey responses from stakeholders can often be labor-intensive and time-consuming. This study explores the integration of Large Language Models (LLMs)--like GPT-4--with human expertise to enhance text analysis of stakeholder interviews regarding K-12 education policy within one U.S. state. Employing a mixed-methods approach, human experts developed a codebook and coding processes as informed by domain knowledge and unsupervised topic modeling results. They then designed prompts to guide GPT-4 analysis and iteratively evaluate different prompts' performances. This combined human-computer method enabled nuanced thematic and sentiment analysis. Results reveal that while GPT-4 thematic coding aligned with human coding by 77.89% at specific themes, expanding to broader themes increased congruence to 96.02%, surpassing traditional Natural Language Processing (NLP) methods by over 25%. Additionally, GPT-4 is more closely matched to expert sentiment analysis than lexicon-based methods. Findings from quantitative measures and qualitative reviews underscore the complementary roles of human domain expertise and automated analysis as LLMs offer new perspectives and coding consistency. The human-computer interactive approach enhances efficiency, validity, and interpretability of educational policy research.