We have performed a kinematically complete experiment for target ionization with simultaneous projectile detachment (TIPD) in 200-keV H− + He collisions. From the data we extracted triple-differential cross sections (TDCSs) for each electron separately. These TDCSs closely resemble corresponding data for single ionization by charged-particle impact. Surprisingly, the contributions from higher-order processes to TIPD, proceeding through two independent interactions of each electron with the core of the respective other collision partner, are found to be somewhat larger than the first-order process proceeding through the electron-electron interaction.