Stable free-standing liquid filaments formed by some layered mesophases of bent-core mesogens are unique structures. Some of their physical properties have been analyzed in recent studies, but their microscopic structure and conditions for stability have still been unclear. We explore details of filament shapes and surface profiles of filaments drawn in liquid crystal phases of bent-core mesogens by AFM and SEM measurements, and we present a microscopic structure model. Conclusions on the stabilizing mechanisms are drawn. Qualitative differences in mechanical properties are found for different mesophases, even though the macroscopic appearance of the filaments is very similar.