We develop a virtual material structure model based on a combination of tessellations and Gaussian random fields for a coating layer of paperboard used for packaging and designed to facilitate printing on the surface. To fit the model to tomographic image data acquired using combined focused ion beam and scanning electron microscopy (FIB-SEM), we introduce a novel method for estimating a covariance function, combined with approximate Bayesian computation (ABC). We demonstrate good agreement with the real material in terms of several microstructural descriptors. We then use the developed model in a computational study to establish structure–property relationships, specifically how permeability varies as a function of porosity, length scale, and other parameters of the virtual structure model. We conclude that the variation in permeability can be explained very well by porosity and descriptors that capture path lengths through the pore system, bottleneck effects, and the specific surface area