Multimodal Anomaly Detection (MMAD) has attracted significant attention in industrial defect inspection as it can simultaneously leverage the complementary information from different modalities to achieve higher-precision detection. Among existing MMAD approaches, dual-branch reverse distillation is widely adopted because of its efficiency in avoiding large-scale data storage. However, it suffers from two key issues. First, the alignment of cross-modal features can lead to a loss of modality-specific characteristics. Second, when one modality indicates normal while another shows anomalies, anomaly detection may be misled by that modality ambiguity. To address these challenges, we propose a Frequency-Aware Multimodal Reverse Distillation (FAMRD) framework from the frequency domain perspective. Specifically, we introduce a frequency spectral feature alignment module that aligns the low- and medium-frequency components across modalities to preserve global shape consistency, while maintaining high-frequency modality-specific details. In addition, we design a frequency spectral anomaly synthesis module. It perturbs the normal feature of one modality to create modality consistent anomalies, fuses it with another modality normal feature to mimic modality ambiguous anomalies, and adds them to the reverse distillation process for decision boundary optimization. Extensive experiments on standard MMAD benchmarks demonstrate that FAMRD achieves competitive performance in both anomaly detection and localization, outperforming state-of-the-art methods.