For the two interface cubic cuts: sc(110) and sc(111) we consider the existence regions of interface spin-waves of a ferromagnetic bilayer film on the two-dimensional Brillouin zone as to their size and shape versus the respective interface related parameters (interface exchange coupling and intrinsic interface anisotropy) applying the approximation of a very thick bilayer film and the method of Brillouin zone mapping (the three (100) interface cubic orientations have been dealt with earlier [Phys. Rev. B 51, 16008 (1995)]). Of particular interest to us still remains the emergence of interface spin-waves induced by varying dynamic quantities such as the in-plane propagation wave vector k_{∥}. Moreover, in our present investigation, we put especial emphasis on the effect exerted on the Brillouin zone mapping by varying (in the plane perpendicular to the film) the configuration angle 𝜗 of the film magnetization with respect to the film normal. We predict the existence of (at the most two) critical angles 𝜗_{c} at which the interface spin-waves emerge. These critical angles are functions of the in-plane wave vector k_{∥} of interface spin-wave propagation along the interface. Finally, we discuss the effects due to the presence of critical angles with a view to their exploitation in experimental measurements.