We extend the orbital-dependent electron tunneling model implemented within the three-dimensional (3D) Wentzel-Kramers-Brillouin (WKB) atom-superposition approach to simulate spin-polarized scanning tunneling microscopy (SP-STM) above magnetic surfaces. The tunneling model is based on the electronic structure data of the magnetic tip and surface obtained from first principles. Applying our method, we analyze the orbital contributions to the tunneling current, and study the nature of atomic contrast reversals occurring on constant-current SP-STM images above the Fe( 11 0) surface. We find an interplay of orbital-dependent tunneling and spin-polarization effects responsible for the contrast inversion, and we discuss its dependence on the bias voltage, on the tip-sample distance, and on the tip orbital composition. (C) 2014 Elsevier B.V. All rights reserved.