  Post-AGB binaries are surrounded by circumbinary disks of gas and dust that
are similar to protoplanetary disks found around young stars. We aim to
understand the structure of these disks and identify the physical phenomena at
play in their very inner regions. We want to understand the disk-binary
interaction and to further investigate the comparison with protoplanetary
disks. We have conducted an interferometric snapshot survey of 23 post-AGB
binaries in the near-infrared (H-band) using VLTI/PIONIER. We have fitted the
multiwavelength visibilities and closure phases with purely geometrical models
with an increasing complexity in order to retrieve the sizes, temperatures and
flux ratios of the different components All sources are resolved and the
different components contributing to the H-band flux are dissected. The
environment of these targets is very complex: 13/23 targets need models with
thirteen or more parameters to fit the data. We find that the inner disk rims
follow and extend the size-luminosity relation established for disks around
young stars with an offset toward larger sizes. The measured temperature of the
near-infrared circumstellar emission of post-AGB binaries is lower (Tsub~1200K)
than for young stars, probably due to a different dust mineralogy and/or gas
density in the dust sublimation region. The dusty inner rims of the
circumbinary disks around post-AGB binaries are ruled by dust sublimation
physics. Additionally, a significant amount of the circumstellar H-band flux is
over-resolved (14 targets have more than 10% of their non-stellar flux
over-resolved) hinting for more structure from a yet unknown origin (disk
structure or outflow). The amount of over-resolved flux is larger than around
young stars. Due to the complexity of these targets, interferometric imaging is
a necessary tool to reveal the interacting inner regions in a model-independent
way.
