Recent advancements in anomaly detection have shifted focus towards Multi-class Unified Anomaly Detection (MUAD), offering more scalable and practical alternatives compared to traditional one-class-one-model approaches. However, existing MUAD methods often suffer from inter-class interference and are highly susceptible to domain shifts, leading to substantial performance degradation in real-world applications. In this paper, we propose a novel robust prompt-driven MUAD framework, called ROADS, to address these challenges. ROADS employs a hierarchical class-aware prompt integration mechanism that dynamically encodes class-specific information into our anomaly detector to mitigate interference among anomaly classes. Additionally, ROADS incorporates a domain adapter to enhance robustness against domain shifts by learning domain-invariant representations. Extensive experiments on MVTec-AD and VISA datasets demonstrate that ROADS surpasses state-of-the-art methods in both anomaly detection and localization, with notable improvements in out-of-distribution settings.