Most post-disaster damage classifiers succeed only when destructive forces leave clear spectral or structural signatures -- conditions rarely present after inundation. Consequently, existing models perform poorly at identifying flood-related building damages. The model presented in this study, Flood-DamageSense, addresses this gap as the first deep-learning framework purpose-built for building-level flood-damage assessment. The architecture fuses pre- and post-event SAR/InSAR scenes with very-high-resolution optical basemaps and an inherent flood-risk layer that encodes long-term exposure probabilities, guiding the network toward plausibly affected structures even when compositional change is minimal. A multimodal Mamba backbone with a semi-Siamese encoder and task-specific decoders jointly predicts (1) graded building-damage states, (2) floodwater extent, and (3) building footprints. Training and evaluation on Hurricane Harvey (2017) imagery from Harris County, Texas -- supported by insurance-derived property-damage extents -- show a mean F1 improvement of up to 19 percentage points over state-of-the-art baselines, with the largest gains in the frequently misclassified "minor" and "moderate" damage categories. Ablation studies identify the inherent-risk feature as the single most significant contributor to this performance boost. An end-to-end post-processing pipeline converts pixel-level outputs to actionable, building-scale damage maps within minutes of image acquisition. By combining risk-aware modeling with SAR's all-weather capability, Flood-DamageSense delivers faster, finer-grained, and more reliable flood-damage intelligence to support post-disaster decision-making and resource allocation.