Dual-energy x-ray imaging is a powerful tool enabling two-component samples to be separated into their constituent objects from two-dimensional images. Phase contrast x-ray imaging can render the boundaries between media of differing refractive indices visible, despite them having similar attenuation properties; this is important for imaging biological soft tissues. We have used a Laue analyser crystal and a monochromatic x-ray source to combine the benefits of both techniques. The Laue analyser creates two distinct phase contrast images that can be simultaneously acquired on a high-resolution detector. These images can be combined to separate the effects of x-ray phase, absorption and scattering and, using the known complex refractive indices of the sample, to quantitatively segment its component materials. We have successfully validated this phase contrast image segmentation (PCIS) using a two-component phantom, containing an iodinated contrast agent, and have also separated the lungs and ribcage in images of a mouse thorax. Simultaneous image acquisition has enabled us to perform functional segmentation of the mouse thorax throughout the respiratory cycle during mechanical ventilation.