What does a typical full disc around a post-AGB binary look like? Radiative transfer models reproducing PIONIER, GRAVITY, and MATISSE data

(abridged) Stable circumbinary discs around evolved post-Asymptotic Giant branch (post-AGB) binary systems show many similarities with protoplanetary discs around young stellar objects. These discs can provide constraints on both binary evolution and the formation of macrostructures within circumstellar discs. Here we focus on one post-AGB binary system: IRAS08544-4431. We aim to refine the physical model of IRAS08544-4431 with a radiative transfer treatment and continue the near-infrared and mid-infrared interferometric analysis covering the H-, K-, L-, and N-bands. We aim to capture the previously detected amount of over-resolved flux and the radial intensity profile at and beyond the inner dust disc rim to put constraints on the physical processes in the inner disc regions. We used a Monte Carlo radiative transfer code to investigate the physical structure of the disc by reproducing both the photometry and the multi-wavelength infrared interferometric data set. We developed a strategy to identify the models which perform best to reproduce our data set. We found a family of models that successfully fit the infrared photometric and interferometric data in all bands. Some over-resolved flux component was recovered in all bands but the optimised models still fall short to explain all the over-resolved flux. This suggests that another dusty structure within the system plays a role. Multi-wavelength infrared interferometric observations of circumstellar discs allow to study the inner disc regions in unprecedented detail. The refined physical models can reproduce most of the investigated features, including the photometric characteristics, the radial extent, and the overall shape of the visibility curves. Our multi-wavelength interferometric observations combined with photometry show that the disc is similar to protoplanetary discs with similar dust masses and efficient dust growth.