Interiors of neutron stars are ultradense and may contain a core of deconfined quark matter. Such a core connects to the outer layers smoothly or through a sharp microscopic interface or through an intermediate macroscopic layer of inhomogeneous mixed phases, which is globally neutral but locally contains electrically charged domains. Here I employ a nucleon-meson model under neutron star conditions that shows a first-order chiral phase transition at large densities. In the vicinity of this chiral transition I calculate the free energies of various mixed phases---different ``pasta structures''---in the Wigner-Seitz approximation. Crucially, chirally broken nuclear matter and the approximately chirally symmetric phase (loosely interpreted as quark matter) are treated on the same footing. This allows me to compute the interface profiles of bubbles, rods, and slabs fully consistently, taking into account electromagnetic screening effects and without needing the surface tension as an input. I find that the full numerical results tend to disfavor mixed phases compared to a simple steplike approximation used frequently in the literature and that the predominantly favored pasta structure consists of slabs with a surface tension $\mathrm{\ensuremath{\Sigma}}\ensuremath{\simeq}6\text{ }\text{ }\mathrm{MeV}/{\mathrm{fm}}^{2}$.