  Aim: We aim to study in detail the peculiar mineralogy and structure of the
circumstellar environment of two binary post-AGB stars, EPLyr and HD52961. Both
stars were selected from a larger sample of evolved disc sources observed with
Spitzer and show unique solid-state and gas features in their infrared spectra.
Moreover, they show a very small infrared excess in comparison with the other
sample stars. Methods: The different dust and gas species are identified on the
basis of high-resolution Spitzer-IRS spectra. We fit the full spectrum to
constrain grain sizes and temperature distributions in the discs. This,
combined with our broad-band spectral energy distribution and interferometric
measurements, allows us to study the physical structure of the disc, using a
self-consistent 2D radiative-transfer disc model. Results: We find that both
stars have strong emission features due to CO_2 gas, dominated by
^{12}C^{16}O_2, but with clear ^{13}C^{16}O_2 and even ^{16}O^{12}C^{18}O
isotopic signatures. Crystalline silicates are apparent in both sources but
proved very hard to model. EP Lyr also shows evidence of mixed chemistry, with
emission features of the rare class-C PAHs. Whether these PAHs reside in the
oxygen-rich disc or in a carbon-rich outflow is still unclear. With the
strongly processed silicates, the mixed chemistry and the low ^{12}C/^{13}C
ratio, EP Lyr resembles some silicate J-type stars, although the depleted
photosphere makes nucleosynthetic signatures difficult to probe. We find that
the disc environment of both sources is, to a first approximation, well
modelled with a passive disc, but additional physics such as grain settling,
radial dust distributions, and an outflow component must be included to explain
the details of the observed spectral energy distributions in both stars.
