With the widespread industrial deployment of Large Language Models (LLMs), DeepSearch has emerged as the dominant paradigm for resolving complex user queries. It implements an iterative closed-loop workflow consisting of planning and reflection, information retrieval, and answer generation. However, existing reward models (RMs) are largely designed for static single-turn tasks, failing to capture the full-pipeline complexity of DeepSearch workflows. To address this limitation, we propose F²DR, a fine-grained full-pipeline reward framework. F²DR evaluates DeepSearch workflows across three dimensions: Content, Trajectory, and Answer, enabling comprehensive process-level assessment. We further construct DeepSearch RM-Bench, a dedicated benchmark for evaluating RMs in DeepSearch scenarios. Extensive experiments demonstrate that F²DR achieves significantly higher evaluation consistency than existing baselines, while DeepSearch RM-Bench exhibits strong discriminative capability across existing open-source RMs. We will publicly release the complete DeepSearch RM-Bench dataset.