Collaborative perception enables agents to share complementary perceptual information with nearby agents. This would improve the perception performance and alleviate the issues of single-view perception, such as occlusion and sparsity. Most existing approaches mainly focus on single modality (especially LiDAR), and not fully exploit the superiority of multi-modal perception. We propose a collaborative perception paradigm, BM2CP, which employs LiDAR and camera to achieve efficient multi-modal perception. It utilizes LiDAR-guided modal fusion, cooperative depth generation and modality-guided intermediate fusion to acquire deep interactions among modalities of different agents, Moreover, it is capable to cope with the special case where one of the sensors, same or different type, of any agent is missing. Extensive experiments validate that our approach outperforms the state-of-the-art methods with 50X lower communication volumes in both simulated and real-world autonomous driving scenarios. Our code is available at https://github.com/byzhaoAI/BM2CP.