We present a method for phase microtomography based on X-ray propagation based phase contrast imaging for multi-material objects. Previously, homogeneous composition assumptions have been in the Radon domain to overcome low sensitivity in the low frequency range. Here, we introduce a prior in the object domain based on multiple, but known, materials in the sample. This is achieved by first reconstructing a tomographic attenuation scan, introducing the prior by segmentation, and finally forward projecting this initial object estimate to yield a priori phase maps. The method is applied to the imaging of a mouse knee where analysis of both soft and hard tissue is of interest, and is shown to perform better than previously proposed methods.