In this study, we propose a novel microstructure-sensitive Bayesian optimization (BO) framework designed to enhance the efficiency of materials discovery by explicitly incorporating microstructural information. Traditional materials design approaches often focus exclusively on direct chemistry-process-property relationships, overlooking the critical role of microstructures. To address this limitation, our framework integrates microstructural descriptors as latent variables, enabling the construction of a comprehensive process-structure-property mapping that improves both predictive accuracy and optimization outcomes. By employing the active subspace method for dimensionality reduction, we identify the most influential microstructural features, thereby reducing computational complexity while maintaining high accuracy in the design process. This approach also enhances the probabilistic modeling capabilities of Gaussian processes, accelerating convergence to optimal material configurations with fewer iterations and experimental observations. We demonstrate the efficacy of our framework through synthetic and real-world case studies, including the design of Mg$_2$Sn$_x$Si$_{1-x}$ thermoelectric materials for energy conversion. Our results underscore the critical role of microstructures in linking processing conditions to material properties, highlighting the potential of a microstructure-aware design paradigm to revolutionize materials discovery. Furthermore, this work suggests that since incorporating microstructure awareness improves the efficiency of Bayesian materials discovery, microstructure characterization stages should be integral to automated -- and eventually autonomous -- platforms for materials development.
