Context : Many post-asymptotic giant branch ( post-AGB ) stars in binary systems have an infrared ( IR ) excess arising from a dusty circumbinary disk .
The disk formation , current structure , and further evolution are , however , poorly understood .

Aims : We aim to constrain the structure of the circumstellar material around the post-AGB binary and RV Tauri pulsator AC Her .
We want to constrain the spatial distribution of the amorphous and of the crystalline dust .

Methods : We present very high-quality mid-IR interferometric data that were obtained with the MIDI/VLTI instrument .
We analyze the MIDI visibilities and differential phases in combination with the full spectral energy distribution ( SED ) , using the MCMax radiative transfer code , to find a good structure model of AC Her ’ s circumbinary disk .
We include a grain size distribution and midplane settling of dust self-consistently in our models .
The spatial distribution of crystalline forsterite in the disk is investigated with the mid-IR features , the 69 \mu m band and the 11.3 \mu m signatures in the interferometric data .

Results : All the data are well fitted by our best model .
The inclination and position angle of the disk are precisely determined at i = 50 \pm 8 ^ { \circ } and PA = 305 \pm 10 ^ { \circ } .
We firmly establish that the inner disk radius is about an order of magnitude larger than the dust sublimation radius .
The best-fit dust grain size distribution shows that significant grain growth has occurred , with a significant amount of mm-sized grains now being settled to the midplane of the disk .
A large total dust mass \geq 10 ^ { -3 } M _ { \odot } is needed to fit the mm fluxes .
By assuming \alpha _ { turb } = 0.01 , a good fit is obtained with a small grain size power law index of 3.25 , combined with a small gas/dust ratio \leq 10 .
The resulting gas mass is compatible with recent estimates employing direct gas diagnostics .
The spatial distribution of the forsterite is different from the amorphous dust , as more warm forsterite is needed in the surface layers of the inner disk .

Conclusions : The disk in the AC Her system is in a very evolved state , as shown by its small gas/dust ratio and large inner hole .
Mid-IR interferometry offers unique constraints , complementary to mid-IR features , for studying the mineralogy in disks .
A better uv coverage is needed to constrain in detail the distribution of the crystalline forsterite in the disk of AC Her , but we find strong similarities with the protoplanetary disk HD100546 .