The Milnor-Hirzebruch class of a locally complete intersection X in an
algebraic manifold M measures the difference between the (Poincare dual of the)
Hirzebruch class of the virtual tangent bundle of X and, respectively, the
Brasselet-Schuermann-Yokura (homology) Hirzebruch class of X. In this note, we
calculate the Milnor-Hirzebruch class of a globally defined algebraic
hypersurface X in terms of the corresponding Hirzebruch invariants of singular
strata in a Whitney stratification of X. Our approach is based on Schuermann's
specialization property for the motivic Hirzebruch class transformation of
Brasselet-Schuermann-Yokura.