Context : Post-AGB binaries are surrounded by circumbinary disks of gas and dust that are similar to protoplanetary disks found around young stars .

Aims : 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 .

Methods : 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 ( including two point-sources , an azimuthally modulated ring and an over-resolved flux ) in order to retrieve the sizes , temperatures and flux ratios of the different components .

Results : 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 ( T _ { \mathrm { sub } } \sim 1200 K ) than for young stars , probably due to a different dust mineralogy and/or gas density in the dust sublimation region .

Conclusions : 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 .