We propose a joint foreground-background mixture model (FBM) that simultaneously performs background estimation and motion segmentation in complex dynamic scenes. Our FBM consist of a set of location-specific dynamic texture (DT) components, for modeling local background motion, and set of global DT components, for modeling consistent foreground motion. We derive an EM algorithm for estimating the parameters of the FBM. We also apply spatial constraints to the FBM using an Markov random field grid, and derive a corresponding variational approximation for inference. Unlike existing approaches to background subtraction, our FBM does not require a manually selected threshold or a separate training video. Unlike existing motion segmentation techniques, our FBM can segment foreground motions over complex background with mixed motions, and detect stopped objects. Since most dynamic scene datasets only contain videos with a single foreground object over a simple background, we develop a new challenging dataset with multiple foreground objects over complex dynamic backgrounds. In experiments, we show that jointly modeling the background and foreground segments with FBM yields significant improvements in accuracy on both background estimation and motion segmentation, compared to state-of-the-art methods.