We present a stochastic model for the microstructure of a ceramic foam filter which is produced by coating an open polymer foam with liquid ceramic. First, we fit a random Laguerre tessellation to the polymer foam skeleton. Then, the coating is modeled using locally adaptable morphology which allows for the reproduction of the ceramic foam's locally varying strut thickness. Furthermore, we introduce methods for the estimation of the intensity and orientation distribution of the closed facets which are formed during the coating process. By computation of the permeability of the foam in different directions we show that the anisostropic behavior of the material is reproduced correctly in the model.