Recent advancements in computer vision and deep learning have enhanced disaster-response capabilities, particularly in the rapid assessment of earthquake-affected urban environments. Timely identification of accessible entry points and structural obstacles is essential for effective search-and-rescue (SAR) operations. To address this need, we introduce DRespNeT, a high-resolution dataset specifically developed for aerial instance segmentation of post-earthquake structural environments. Unlike existing datasets, which rely heavily on satellite imagery or coarse semantic labeling, DRespNeT provides detailed polygon-level instance segmentation annotations derived from high-definition (1080p) aerial footage captured in disaster zones, including the 2023 Turkiye earthquake and other impacted regions. The dataset comprises 28 operationally critical classes, including structurally compromised buildings, access points such as doors, windows, and gaps, multiple debris levels, rescue personnel, vehicles, and civilian visibility. A distinctive feature of DRespNeT is its fine-grained annotation detail, enabling differentiation between accessible and obstructed areas, thereby improving operational planning and response efficiency. Performance evaluations using YOLO-based instance segmentation models, specifically YOLOv8-seg, demonstrate significant gains in real-time situational awareness and decision-making. Our optimized YOLOv8-DRN model achieves 92.7% mAP50 with an inference speed of 27 FPS on an RTX-4090 GPU for multi-target detection, meeting real-time operational requirements. The dataset and models support SAR teams and robotic systems, providing a foundation for enhancing human-robot collaboration, streamlining emergency response, and improving survivor outcomes.