The rendering of a same printed image can change drastically considering the large number of different types of print support (paper, metallic panel, textile, plastic, etc.) and different types of inks (dye based, pigment based, etc.). Predicting the visual rendering of inks printed on any support by characterizing separately the spectral properties of the inks and those of the print support has been for a while an objective for the printing community. In this paper, we propose a multiscale solution to this issue which combines optical models and measurements. On the one side, we predict the reflectance and transmittance of ink layers alone (without support) by using a radiative transfer four-flux model based on the microscopic characteristics of the inks. On the other side, the reflectance and transmittance of the print support are obtained directly through macroscopic measurements. Finally, through the four-flux matrix model, we compute the joint reflectance and transmittance of the superposition of the stack of inks on the support. Initial results show that the proposed approach is suitable for the prediction of image rendering on different combinations of ink and print support.