Multimodal sensing systems are increasingly prevalent in various real-world applications. Most existing multimodal learning approaches heavily rely on training with a large amount of complete multimodal data. However, such a setting is impractical in real-world IoT sensing applications where data is typically collected by distributed nodes with heterogeneous data modalities, and is also rarely labeled. In this paper, we propose MMBind, a new framework for multimodal learning on distributed and heterogeneous IoT data. The key idea of MMBind is to construct a pseudo-paired multimodal dataset for model training by binding data from disparate sources and incomplete modalities through a sufficiently descriptive shared modality. We demonstrate that data of different modalities observing similar events, even captured at different times and locations, can be effectively used for multimodal training. Moreover, we propose an adaptive multimodal learning architecture capable of training models with heterogeneous modality combinations, coupled with a weighted contrastive learning approach to handle domain shifts among disparate data. Evaluations on ten real-world multimodal datasets highlight that MMBind outperforms state-of-the-art baselines under varying data incompleteness and domain shift, and holds promise for advancing multimodal foundation model training in IoT applications.