This paper proposes a novel, theoretically rigorous deep learning framework designed to maintain high classification and estimation accuracy in environments where standard RGB data is insufficient, corrupted, or unavailable. While state-of-the-art Convolutional Neural Networks (CNNs) excel in varied visual recognition tasks, they often struggle with domain shifts-such as those found in thermal, depth, or low-light imagery-and scenarios characterized by severe data scarcity. We introduce a "Semiparallel Hybrid Architecture" (SHA) that utilizes Cross-Modal Feature Distillation (CMFD) to bridge the semantic gap between varying image modalities. The proposed method employs a dual-stream encoder mechanism fused via a learned Semiparallel Attention Mechanism (SAM), demonstrating superior performance in extracting latent features for biometric security, medical diagnostics, and geometric estimation. Beyond empirical validation, we provide a comprehensive mathematical analysis of the system, employing Information Bottleneck theory to prove that our distillation objective maximizes the relevant mutual information while compressing nuisance variables. We further derive generalization bounds based on Rademacher complexity for the proposed multi-modal hypothesis space. Extensive experiments across three distinct domains-biometrics, medical diagnostics, and monocular depth estimation-reveal that our framework outperforms existing benchmarks, achieving a 14.3% improvement in depth estimation accuracy (RMSE) and a 9.2% increase in F1-score for low-data medical classification tasks compared to standard transfer learning approaches.