Accurately predicting antibody-antigen binding residues, i.e., paratopes and epitopes, is crucial in antibody design. However, existing methods solely focus on uni-modal data (either sequence or structure), disregarding the complementary information present in multi-modal data, and most methods predict paratopes and epitopes separately, overlooking their specific spatial interactions. In this paper, we propose a novel Multi-modal contrastive learning and Interaction informativeness estimation-based method for Paratope and Epitope prediction, named MIPE, by using both sequence and structure data of antibodies and antigens. MIPE implements a multi-modal contrastive learning strategy, which maximizes representations of binding and non-binding residues within each modality and meanwhile aligns uni-modal representations towards effective modal representations. To exploit the spatial interaction information, MIPE also incorporates an interaction informativeness estimation that computes the estimated interaction matrices between antibodies and antigens, thereby approximating them to the actual ones. Extensive experiments demonstrate the superiority of our method in predicting paratopes and epitopes compared to baselines. Additionally, the ablation studies and visualizations demonstrate the superiority of MIPE owing to the better representations acquired through multi-modal contrastive learning and the interaction patterns comprehended by the interaction informativeness estimation.