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.
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