The angular and energy dependencies of the exchange interaction between the electrons in an itinerant ferromagnetic surface can be mapped out by exciting two interacting spin-polarized electrons into the vacuum and resolving at the same time the energies and emission angles of the two electrons. From a tensorial symmetry analysis it is deduced that the recorded two-particle spectra carry detailed information on the spin-split electronic structure that can be extracted under favorable conditions. To substantiate these statements we present and analyze experimental results and numerical calculations for a ferromagnetic iron surface.