Infrared and visible image fusion (IVIF) faces significant challenges in effectively extracting complementary features while suppressing redundant information. To address this, we propose BCIMFuse, a two-stage fusion framework that enhances both intra- and inter-modal relationships. In the first stage, coarse-to-fine bimodal representation learning is performed. In the second stage, we introduce two novel components: the Intra-modal Enhanced Representation Learning (IERL) module to strengthen intra-modal feature discrimination, and the Inter-modal Complementary Relation Progressive Mining (ICRPM) module to iteratively extract cross-modal semantic-level complementary features while reducing redundancy. Experimental results on multiple public datasets demonstrate that BCIMFuse consistently outperforms existing state-of-the-art methods in both visual quality and quantitative metrics, offering a more effective and robust solution for IVIF tasks.