Monocular cameras are attractive for robotic perception due to their low cost and ease of deployment, yet achieving reliable real-time spatial understanding from a single image stream remains challenging. While recent multi-task dense prediction models have improved per-pixel depth and semantic estimation, translating these advances into stable monocular mapping systems is still non-trivial. This paper presents M2H-MX, a real-time multi-task perception model for monocular spatial understanding. The model preserves multi-scale feature representations while introducing register-gated global context and controlled cross-task interaction in a lightweight decoder, enabling depth and semantic predictions to reinforce each other under strict latency constraints. Its outputs integrate directly into an unmodified monocular SLAM pipeline through a compact perception-to-mapping interface. We evaluate both dense prediction accuracy and in-the-loop system performance. On NYUDv2, M2H-MX-L achieves state-of-the-art results, improving semantic mIoU by 6.6% and reducing depth RMSE by 9.4% over representative multi-task baselines. When deployed in a real-time monocular mapping system on ScanNet, M2H-MX reduces average trajectory error by 60.7% compared to a strong monocular SLAM baseline while producing cleaner metric-semantic maps. These results demonstrate that modern multi-task dense prediction can be reliably deployed for real-time monocular spatial perception in robotic systems.