In the standard theory of electroweak interaction with nonperturbative regime, Z-bosons scattering with the exchange of Higgs bosons are studied. Using ladder diagrams approximations, Bethe-Salpeter type integral equations with minimally perturbative kernels for scattering amplitudes are formulated. In the Regge regions of energy changes, asymptotic solutions of the corresponding Bethe-Salpeter equations for the imaginary part of scattering amplitudes in the form of power functions are found.