Histologic assessment of stromal tumor infiltrating lymphocytes (sTIL) as a surrogate of the host immune response has been shown to be prognostic and potentially chemo-predictive in triple-negative and HER2-positive breast cancers. The current practice of manual assessment is prone to intra- and inter-observer variability. Furthermore, the inter-play of sTILs, tumor cells, other microenvironment mediators, their spatial relationships, quantity, and other image-based features have yet to be determined exhaustively and systemically. Towards analysis of these aspects, we developed a deep learning based method for joint region-level and nucleus-level segmentation and classification of breast cancer H&E tissue whole slide images. Our proposed method simultaneously identifies tumor, fibroblast, and lymphocyte nuclei, along with key histologic region compartments including tumor and stroma. We also show how the resultant segmentation masks can be combined with seeding approaches to yield accurate nucleus classifications. Furthermore, we outline a simple workflow for calibrating computational scores to human scores for consistency. The pipeline identifies key compartments with high accuracy (Dice= overall: 0.78, tumor: 0.83, and fibroblasts: 0.77). ROC AUC for nucleus classification is high at 0.89 (micro-average), 0.89 (lymphocytes), 0.90 (tumor), and 0.78 (fibroblasts). Spearman correlation between computational sTIL and pathologist consensus is high (R=0.73, p<0.001) and is higher than inter-pathologist correlation (R=0.66, p<0.001). Both manual and computational sTIL scores successfully stratify patients by clinical progression outcomes.