Autonomous systems, such as self-driving cars, rely on reliable semantic environment perception for decision making. Despite great advances in video semantic segmentation, existing approaches ignore important inductive biases and lack structured and interpretable internal representations. In this work, we propose MCDS-VSS, a structured filter model that learns in a self-supervised manner to estimate scene geometry and ego-motion of the camera, while also estimating the motion of external objects. Our model leverages these representations to improve the temporal consistency of semantic segmentation without sacrificing segmentation accuracy. MCDS-VSS follows a prediction-fusion approach in which scene geometry and camera motion are first used to compensate for ego-motion, then residual flow is used to compensate motion of dynamic objects, and finally the predicted scene features are fused with the current features to obtain a temporally consistent scene segmentation. Our model parses automotive scenes into multiple decoupled interpretable representations such as scene geometry, ego-motion, and object motion. Quantitative evaluation shows that MCDS-VSS achieves superior temporal consistency on video sequences while retaining competitive segmentation performance.