Breast cancer diagnosis relies on immunohistochemistry (IHC) to assess key biomarkers, including estrogen receptor (ER), progesterone receptor (PR), human epidermal growth factor receptor 2 (HER2), and Ki-67, which are essential for clinical decision-making. In this study, we present a hybrid framework that integrates differential equation–based tumor modeling with interpretable deep learning for automated analysis of IHC whole-slide images. Convolutional neural networks (CNNs) are employed to extract discriminative histopathological features, while graph neural networks (GNNs) explicitly model spatial relationships and interactions among individual cells. To incorporate biological plausibility, the proposed architecture is guided by mechanistic insights derived from ordinary and partial differential equation (ODE/PDE) models describing tumor growth and biomarker diffusion, implemented through physics-informed learning constraints. Interpretability is a central design objective. Attention mechanisms and saliency-based visualization techniques are used to highlight spatial biomarker patterns and cell-level features that drive model predictions, enabling transparent and clinically meaningful explanations. The framework is evaluated on publicly available breast cancer IHC datasets, including ACROBAT and AIDPATH, as well as custom multi-stain collections with paired H&E and IHC images. Experimental results demonstrate that the proposed approach achieves state-of-the-art diagnostic performance while providing intuitive explanations of tumor phenotype, such as receptor status and tumor grade, based on spatially distributed biomarkers. By unifying mechanistic mathematical modeling with interpretable deep learning, this work advances both clinical deployment and research in digital pathology.