Motivation: Integrating multimodal data represents an effective approach to predicting biomedical characteristics, such as protein functions and disease outcomes. However, existing data integration approaches do not sufficiently address the heterogeneous semantics of multimodal data. In particular, early and intermediate approaches that rely on a uniform integrated representation reinforce the consensus among the modalities but may lose exclusive local information. The alternative late integration approach that can address this challenge has not been systematically studied for biomedical problems. Results: We propose Ensemble Integration (EI) as a novel systematic implementation of the late integration approach. EI infers local predictive models from the individual data modalities using appropriate algorithms and uses heterogeneous ensemble algorithms to integrate these local models into a global predictive model. We also propose a novel interpretation method for EI models. We tested EI on the problems of predicting protein function from multimodal STRING data and mortality due to coronavirus disease 2019 (COVID-19) from multimodal data in electronic health records. We found that EI accomplished its goal of producing significantly more accurate predictions than each individual modality. It also performed better than several established early integration methods for each of these problems. The interpretation of a representative EI model for COVID-19 mortality prediction identified several disease-relevant features, such as laboratory test (blood urea nitrogen and calcium) and vital sign measurements (minimum oxygen saturation) and demographics (age). These results demonstrated the effectiveness of the EI framework for biomedical data integration and predictive modeling.