Comprehensive fully differential cross sections for electron emission into all three spatial dimensions are presented for 1 keV and 102 eV electron-impact single ionization of helium using an advanced reaction microscope. Surprising out-of-plane contributions, traced back to an interference term in a perturbation expansion by comparison with ion-impact data, severely challenge theoretical models that accurately predict coplanar emission. The data represent the ultimate benchmark for recently developed exact theoretical descriptions of the most fundamental three-body quantum problems.