Persona-driven role-playing (PRP) aims to build AI characters that can respond to user queries by faithfully sticking with \emph{all} (factual) statements in persona documents.Unfortunately, existing faithfulness criteria for PRP are limited to coarse-grained LLM-based scoring without a clear definition or formulation.This paper presents a pioneering exploration to quantify PRP faithfulness evaluation as a fine-grained and explainable criterion, which also serves as a reliable reference for faithfulness optimization.Our criterion first discriminates persona statements into \emph{active} and \emph{passive} constraints by identifying the query-statement relevance.Then, we incorporate all constraints following the principle that the AI character's response should be (a) entailed by active constraints and (b) not contradicted by passive constraints.We translate this principle mathematically into a novel Active-Passive-Constraint (APC) score, a constraint-wise sum of statement-to-response natural language inference (NLI) scores weighted by constraint-query relevance scores. In practice, we build the APC scoring system by symbolically distilling small NLI and relevance discriminators (300M parameters) from GPT-4 for efficiency, and both show high consistency with GPT-4's discrimination.We validate the quality of the APC score against human evaluation based on example personas with tens of statements, and the results show a high correlation.As the APC score could faithfully reflect the PRP quality, we further leverage it as a reward system in direct preference optimization (DPO) for better AI characters. Our experiments offer a fine-grained and explainable comparison between existing PRP techniques, revealing their advantages and limitations.We further find APC-based DPO to be one of the most competitive techniques for sticking with all constraints and can be well incorporated with other techniques.We then extend the scale of the experiments to real persons with hundreds of statements and reach a consistent conclusion. Finally, we provide comprehensive analyses and case studies to support the effectiveness of APC and APC-based DPO.