The morphology of block copolymers (BCPs) critically influences material properties and applications. This work introduces a machine learning (ML)-enabled, high-throughput framework for analyzing grazing incidence small-angle X-ray scattering (GISAXS) data and atomic force microscopy (AFM) images to characterize BCP thin film morphology. A convolutional neural network was trained to classify AFM images by morphology type, achieving 97% testing accuracy. Classified images were then analyzed to extract 2D grain size measurements from the samples in a high-throughput manner. ML models were developed to predict morphological features based on processing parameters such as solvent ratio, additive type, and additive ratio. GISAXS-based properties were predicted with strong performances ($R^2$ > 0.75), while AFM-based property predictions were less accurate ($R^2$ < 0.60), likely due to the localized nature of AFM measurements compared to the bulk information captured by GISAXS. Beyond model performance, interpretability was addressed using Shapley Additive exPlanations (SHAP). SHAP analysis revealed that the additive ratio had the largest impact on morphological predictions, where additive provides the BCP chains with increased volume to rearrange into thermodynamically favorable morphologies. This interpretability helps validate model predictions and offers insight into parameter importance. Altogether, the presented framework combining high-throughput characterization and interpretable ML offers an approach to exploring and optimizing BCP thin film morphology across a broad processing landscape.