Simultaneous ionization and excitation of helium atoms by 500 eV electron impact is observed by a triple coincidence of an ionized slow electron, the recoiling He+ ion, and the radiated vacuum ultraviolet photon (lambda< or =30.4 nm). Kinematically complete differential cross sections are presented for the He+(2p)2P final ionic state, demonstrating the feasibility of a quantum mechanically complete experiment. The experimental data are compared to predictions from state-of-the-art numerical calculations. For large momentum transfers, a first-order treatment of the projectile-target interaction can reproduce the experimental angular dependence, but a second-order treatment is required to obtain consistent magnitudes.