Human intelligence is multimodal; we integrate visual, linguistic, and acoustic signals to maintain a holistic worldview. Most current pretraining methods, however, are limited to one or two modalities. We present i-Code, a self-supervised pretraining framework where users may flexibly combine the modalities of vision, speech, and language into unified and general-purpose vector representations. In this framework, data from each modality are first given to pretrained single-modality encoders. The encoder outputs are then integrated with a multimodal fusion network, which uses novel attention mechanisms and other architectural innovations to effectively combine information from the different modalities. The entire system is pretrained end-to-end with new objectives including masked modality unit modeling and cross-modality contrastive learning. Unlike previous research using only video for pretraining, the i-Code framework can dynamically process single, dual, and triple-modality data during training and inference, flexibly projecting different combinations of modalities into a single representation space. Experimental results demonstrate how i-Code can outperform state-of-the-art techniques on five video understanding tasks and the GLUE NLP benchmark, improving by as much as 11% and demonstrating the power of integrative multimodal pretraining.