We present a study of Hen 2-155 and Hen 2-161, two planetary nebulae which bear striking morphological similarities to other planetary nebulae known to host close-binary central stars. Both central stars are revealed to be photometric variables while spectroscopic observations confirm that Hen 2-155 is host to a double-eclipsing, post-common-envelope system with an orbital period of 3h33m making it one of the shortest period binary central stars known. The observations of Hen 2-161 are found to be consistent with a post-common-envelope binary of period ~1 day. A detailed model of the central star of Hen 2-155 is produced, showing the nebular progenitor to be a hot, post-AGB remnant of approximately 0.62 M⊙, consistent with the age of the nebula, and the secondary star to be an M dwarf whose radius is almost twice the expected zero age main sequence radius for its mass. In spite of the small numbers, all main-sequence companions, of planetary nebulae central stars, to have had their masses and radii constrained by both photometric and spectroscopic observations have also been found to display this "inflation". The cause of the "inflation" is uncertain but is probably related to rapid accretion, immediately before the recent common-envelope phase, to which the star has not yet thermally adjusted. The chemical composition of both nebulae is also analysed, showing both to display elevated abundance discrepancy factors. This strengthens the link between elevated abundance discrepancy factors and close binarity in the nebular progenitor. Full Tables 2-5, and 7 are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/580/A19