Membrane-active antibiotics are known to selectively target certain pathogens based on cell membrane properties, such as fluidity, lipid ordering, and phase behavior. These are in turn modulated by the composition of a lipid bilayer and in particular by the presence and type of membrane sterols. Amphotericin B (AmB), the golden standard of antifungal treatment, exhibits higher activity toward ergosterol-rich fungal membranes, which permits its use against systemic mycoses; however, the selectivity for fungal membranes is far from satisfactory leading to severe side effects. Despite decades of research, no consensus has emerged on the origin of AmB specificity for fungal cells and its actual mode of action at the molecular level. Previously, it has been proposed that the specific action of AmB is related to differences in its affinity for membranes of different composition. In this work, we investigate this relationship by employing molecular dynamics simulations to compare the free energy of insertion of AmB into three types of membranes: a pure DMPC bilayer and DMPC bilayers containing 30% of cholesterol or ergosterol. We analyze the orientation of AmB molecules within the bilayer in order to unambiguously establish their membrane binding mode and relate the orientational freedom to the sterol-dependent tightness of lipid packing. Our results strongly indicate that the membrane insertion of AmB proceeds virtually to completion independent of membrane type, and hence the higher toxicity against fungal membranes may rather result from differences in subsequent oligomerization in the membrane and assembly of monomers into functional transmembrane pores. In particular, the latter could be facilitated by sterol-induced ordering of AmB molecules along the membrane normal, revealed by our free energy profiles. Moreover--in contrast to certain claims--we find no stable binding mode corresponding to the horizontal adsorption of AmB on the membrane surface.