The influence of interfaces on the perpendicular magnetic anisotropy (PMA) in evaporated Tb/bcc-Fe multilayers with and without diamagnetic Y blocking layers, {Tb/Fe/Y}(10) [=Y(1), Fe-on-Tb], {Y/Fe/Tb}(10) [=Y(2), Tb-on-Fe] and {Tb/Fe}(10) [=Y(3)], is investigated using torque magnetometry as a function of the angle a between the applied field H and the film plane at temperatures 15 K less than or equal to T less than or equal to 300 K. Interface-induced PMA becomes noticeable below the ordering temperatures of the TbFe alloy in the rough Tb/Fe interfaces of Y(1) (T(c)greater than or equal to 300 K) and that of Tb at the smooth Tb/Fe interfaces of Y(2) (T-c=219 K). The latter mechanism dominates at low T, as explained within the framework of a coupled layer model, which is also able to describe the magnetic cone states found in Y(1), Y(2), and Y(3) at T<100 K. In Y(3) the PMA is significantly enhanced by interlayer coupling, leading to polar cone angles as small as 30 degrees.