Robust semantic perception for autonomous vehicles relies on effectively combining multiple sensors with complementary strengths and weaknesses. State-of-the-art sensor fusion approaches to semantic perception often treat sensor data uniformly across the spatial extent of the input, which hinders performance when faced with challenging conditions. By contrast, we propose a novel depth-guided multimodal fusion method that upgrades condition-aware fusion by integrating depth information. Our network, DGFusion, poses multimodal segmentation as a multi-task problem, utilizing the lidar measurements, which are typically available in outdoor sensor suites, both as one of the model's inputs and as ground truth for learning depth. Our corresponding auxiliary depth head helps to learn depth-aware features, which are encoded into spatially varying local depth tokens that condition our attentive cross-modal fusion. Together with a global condition token, these local depth tokens dynamically adapt sensor fusion to the spatially varying reliability of each sensor across the scene, which largely depends on depth. In addition, we propose a robust loss for our depth, which is essential for learning from lidar inputs that are typically sparse and noisy in adverse conditions. Our method achieves state-of-the-art panoptic and semantic segmentation performance on the challenging MUSES and DeLiVER datasets. Code and models are available at https://github.com/timbroed/DGFusion