In previous experiments on electron-induced two-electron emission from the ferromagnetic surface system Co/W(110), spin-orbit coupling effects have been observed, which are comparable in size to the magnetic exchange effects. The present theoretical work aims at a detailed understanding of such effects, in particular their relation to the spin-dependent electronic structure and to collision dynamics. To this end, we have developed a formalism, which is based on a Dirac equation with an effective magnetic field. Magnetic exchange and spin-orbit coupling are thus incorporated simultaneously. Typical numerical two-electron emission results are presented for W(110) and for ultrathin Co films on W(110) together with the underlying spin- and layer-resolved valence electron spectral density.More detailed insight is provided by calculations, in which SOC was selectively switched off for the valence electron and for the primary and emitted electrons. Our theoretical results are in overall agreement with the experimental data. Furthermore, we predict sizable magnetic dichroism.