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Accurate medical image segmentation commonly requires effective learning of the complementary information from multimodal data. However, in clinical practice, we often encounter the problem of missing imaging modalities. We tackle this challenge and propose a novel multimodal segmentation framework which is robust to the absence of imaging modalities. Our network uses feature disentanglement to decompose the input modalities into the modality-specific appearance code, which uniquely sticks to each modality, and the modality-invariant content code, which absorbs multimodal information for the segmentation task. With enhanced modality-invariance, the disentangled content code from each modality is fused into a shared representation which gains robustness to missing data. The fusion is achieved via a learning-based strategy to gate the contribution of different modalities at different locations. We validate our method on the important yet challenging multimodal brain tumor segmentation task with the BRATS challenge dataset. With competitive performance to the state-of-the-art approaches for full modality, our method achieves outstanding robustness under various missing modality(ies) situations, significantly exceeding the state-of-the-art method by over 16% in average for Dice on whole tumor segmentation.