Accurate prediction of patient drug response is critical for precision cancer medicine but remains constrained by limited clinical data. While in vitro cell line data offer a scalable alternative, effective cross-domain transfer remains challenging. Many existing methods tend to overlook heterogeneous domain shifts across biological contexts, underrepresent the intrinsic differences between cell lines and patient tissues, and insufficiently capture high-order gene-drug interactions. To address these challenges, we propose MACB-DRP, a hierarchical transfer learning framework comprising three complementary stages that progressively coordinate adaptation across tissue, drug, and sample levels while enabling representation separation. The framework begins with tissue-aware domain adaptation, leveraging cancer-type classification and unsupervised alignment to preserve biologically meaningful structure across domains. It then incorporates drug-conditioned adversarial transfer for distribution alignment, coupled with bilinear fusion to model nonlinear and high-order gene-drug interactions. Finally, contrastive anchoring with feature-matched pairs enables fine-grained sample-level alignment, while feature-mismatched negatives preserve irreducible biological disparities. Experimental evaluation demonstrates that MACB-DRP achieves comprehensive predictive performance for patient drug responses, with robust results across multiple cancer types and nine drugs, and further reveals hierarchical structure across drugs and tissues in the visualization. These findings highlight the potential of biologically guided domain adaptation for improving translational pharmacogenomics.