Large multimodal models (LMMs) have demonstrated excellent capabilities in both understanding and generation tasks with various modalities. While these models can accept flexible combinations of input data, their training efficiency suffers from two major issues: pipeline stage imbalance caused by heterogeneous model architectures, and training data dynamicity stemming from the diversity of multimodal data. In this paper, we present DIP, a dynamic and modality-aware pipeline scheduling framework designed for LMM training. DIP tackles the challenge of dynamic imbalance via two key techniques: (1) separating computations of different modalities into dedicated pipeline segments to balance workloads within a continuous set of stages; (2) dynamically splitting input data into finer-grained, modality-specific sub-microbatches to balance workloads across these segments. By asynchronously generating pipeline schedules on idle CPU resources during training, DIP dynamically tailors stage executions to each input batch without stalling the training process. We validate DIP on a diverse set of five LMMs, ranging from 12B to 94B parameters and including vision-language and diffusion models. Experimental results show that our system achieves up to 97.3% higher throughput compared to state-of-the-art systems, demonstrating strong adaptability to fluctuating multimodal training workloads.