Automated radiology report generation (R2Gen) has advanced significantly, introducing challenges in accurate evaluation due to its complexity. Traditional metrics often fall short by relying on rigid word-matching or focusing only on pathological entities, leading to inconsistencies with human assessments. To bridge this gap, we introduce ReFINE, an automatic evaluation metric designed specifically for R2Gen. Our metric utilizes a reward model, guided by our margin-based reward enforcement loss, along with a tailored training data design that enables customization of evaluation criteria to suit user-defined needs. It not only scores reports according to user-specified criteria but also provides detailed sub-scores, enhancing interpretability and allowing users to adjust the criteria between different aspects of reports. Leveraging GPT-4, we designed an easy-to-use data generation pipeline, enabling us to produce extensive training data based on two distinct scoring systems, each containing reports of varying quality along with corresponding scores. These GPT-generated reports are then paired as accepted and rejected samples through our pairing rule to train an LLM towards our fine-grained reward model, which assigns higher rewards to the report with high quality. Our reward-control loss enables this model to simultaneously output multiple individual rewards corresponding to the number of evaluation criteria, with their summation as our final ReFINE. Our experiments demonstrate ReFINE's heightened correlation with human judgments and superior performance in model selection compared to traditional metrics. Notably, our model provides both an overall score and individual scores for each evaluation item, enhancing interpretability. We also demonstrate its flexible training across various evaluation systems.