Development of perpendicular magnetic anisotropy thin films is a requisite for many applications. In this work, we have illustrated the enhancement of the PMA of Hard (Co)/Soft (Permalloy, Py) ferromagnetic bilayers by depositing them onto nanoporous anodic alumina membranes with different hole diameters varying in the range between 30 nm and 95 nm. A dramatic change in the hysteresis loops behaviour with hole size, D, and magnetic surface cover ratio parameters has been observed: (1) for samples with small antidot hole diameters, the in-plane (INP) hysteresis loops show single-step magnetic behaviour; (2) for D = 75 nm, the hysteresis loops of Co/Py and Py samples exhibit a multistep magnetic behaviour; (3) a decreasing coercivity in the INP hysteresis loops for antidot arrays samples with D> 75 nm has been detected as a consequence of the reduction of the INP magnetic anisotropy and the rising of the out-of-plane component. A crossover of the magnetic anisotropy from the INP to out-of-plane for bilayer antidot samples has been observed for Co/Py ferromagnetic bilayers, favoured by the interfacial exchange coupling between the two ferromagnetic materials. These findings can be of high interest for the development of novel magnetic sensors and for perpendicular-magnetic recording patterned media based on template-assisted deposition techniques.