  Many properties of circumbinary discs around evolved post-asymptotic giant
branch (post-AGB) binary systems are similar to those of protoplanetary discs
around young stars. The deficits of near-infrared (near-IR) flux in the
spectral energy distributions (SEDs) of these systems hints towards large
dust-free cavities that are reminiscent of transition discs as are commonly
observed around young stars. We aim to assess the size of the inner rim of 6
post-AGB binary systems with lack in the near-IR like this. We used resolved
mid-infrared (mid-IR) high-angular resolution observations of VLTI/MATISSE and
VLTI/MIDI. We compared these inner rim sizes to 5 systems with available
MATISSE data that were identified to host a disc starting at the dust
sublimation radius. We used geometric ring models to estimate the inner rim
sizes, the relative flux contributions of the star, the ring, and an
over-resolved emission, the orientation of the ring, and the spectral
dependences of the components. We find that the inner dust rims of the targets
with a lack of near-IR excess in their SEDs are 2.5 to 7.5 times larger than
the theoretical dust sublimation radii, and inner rim sizes of the systems that
do not show this deficit are similar to those of their theoretical dust
sublimation radii. The physical radii of the inner rims of these transition
discs around post-AGB binaries are 3-25 au, which are larger than the disc
sizes inferred for transition discs around young stars with VLTI/MIDI. With
mid-IR interferometric data, we directly confirm the transition disc nature of
six circumbinary discs around post-AGB binary systems. Future observational and
modelling efforts are needed to progress in our understanding of the structure,
origin, and evolution of these transition discs
