Given that a majority of stars form in multiple systems, in order to fully understand the star- and planet-formation processes we must seek to understand them in multiple stellar systems. With this in mind, we present an analysis of the enigmatic binary T-Tauri system VV Corona Australis, in which both components host discs, but only one is visible at optical wavelengths. We seek to understand the peculiarities of this system by searching for a model for the binary which explains all the available continuum observations of the system. We present new mid-infrared interferometry and near-infrared spectroscopy along with archival millimetre-wave observations, which resolve the binary at 1.3mm for the first time. We compute a grid of pre-main-sequence radiative transfer models and calculate their posterior probabilities given the observed spectral energy distributions and mid-infrared interferometric visibilities of the binary components, beginning with the assumption that the only differences between the two components are their inclination and position angles. Our best-fitting solution corresponds to a relatively low luminosity T-tauri binary, with each component's disc having a large scale height and viewed at moderate inclination ($\sim 50^\circ$), with the infrared companion inclined by $\sim 5^\circ$ degrees more than the primary. Comparing the results of our model to evolutionary models suggests stellar masses $\sim 1.7$M$_\odot$ and an age for the system of 3.5Myr, towards the upper end of previous estimates. Combining these results with accretion indicators from near-IR spectroscopy, we determine an accretion rate of 4.0$\times 10^{-8}$M$_\odot$ yr$^{-1}$ for the primary. We suggest that future observations of VV~CrA and similar systems should prioritise high angular resolution sub-mm and near-IR imaging of the discs and high resolution optical/NIR spectroscopy of the central stars.