The detailed expressions of orientation-related relative permeability in amorphous alloy ribbons and films with in-plane nearly transverse uniaxial anisotropy under applied driving ac current flowing through the ferromagnetic materials and dc external magnetic field are derived by simultaneously solving the Maxwell's equations and the Landau-Lifshitz equation of motion and establishing the magnetic domain structure model. The calculation formula of mean relative permeability averaging over 90°orientation angle and the magneto-impedance are obtained. The relation between permeability and the component of tensor susceptibility is deduced. The dependences of the real part and imaginary part of the relative permeability on frequency at several values of the applied external field are calculated, and the corresponding magnetic permeability spectra are plotted. The calculation formula of permeability which were inferred by Panina et al and Kraus can be unified by our theoretical result which is in good agreement with the experimental data under lower external magnetic field for both amorphous ribbons and films.