Road-network extraction from very high-resolution (VHR) remote-sensing imagery remains a challenging task owing to the structural sparsity, topological complexity, and severe occlusions of road networks. Conventional graph-based approaches preserve topological consistency yet incur considerable computational overhead, whereas prevailing convolutional neural network (CNN) and Transformer architectures struggle to reconcile long-range contextual modeling with computational efficiency. To address these limitations, this study proposes RFM-UNet, a hybrid frequency and state–space network designed for road-network segmentation. Specifically, the encoder integrates Mamba blocks with an Anisotropic Directional Attention (ADA) module to jointly capture local geometric cues and global dependencies at linear computational complexity. In addition, a Multi-Scale Adaptive Fusion Module (MAFM) is introduced to dynamically recalibrate multi-stage features, thereby suppressing cross-scale interference and preserving the connectivity of narrow roads. To enhance robustness against shadow-induced occlusions, a Dual-Spectrum Aggregation Module (DualSpec) decouples the phase and amplitude spectra in the frequency domain and fuses them with spatial features, effectively mitigating spurious responses and background noise characterized by similar textures. Quantitative and qualitative experiments on three public datasets demonstrate that RFM-UNet consistently outperforms current state-of-the-art methods.