This paper proposes a new approach for improving robotic manipulation tasks that require both precision and high compliance through multisensory fusion. By integrating visual, force, and tactile feedback, our approach enhances performance in delicate insertion tasks. We introduce a unified framework that combines information from these sensors to guide the entire manipulation strategies. Experiments in simulated and physical environments demonstrate that our method outperforms traditional single and dual-modality approaches regarding precision, gentle interactions, and robustness. We also provide a detailed analysis of the results to examine the role of each modality during manipulation.