We studied mixtures of the achiral bent-core mesogen NOBOW 1,3-phenylene bis[4-(4-9-alkoxyphenyliminonetyl)benzoates] (P-9-O-PIMB) and the small, rodlike liquid crystal 8CB using high-resolution synchrotron x-ray diffraction, freeze fracture transmission electron microscopy, and differential scanning calorimetry. NOBOW and 8CB mix in an isotropic state at high temperatures but phase separate at lower temperatures when NOBOW transforms into the B4 phase and forms chiral helical nanofilaments. In pure NOBOW, the nanofilaments are close packed but at moderate 8CB concentrations, they are separated by nanosized gaps filled by 8CB. At higher concentrations of 8CB, macroscopic phase separation occurs.