The quantum-mechanical transmission process of a photoelectron through a surface leaves distinctive marks in the electron momentum distribution emitted from a crystal. By energy-resolved measurements of the complete photoemission half-space above a Cu(001) surface using a momentum microscope, we identify the two-path interference of directly emitted photoelectrons and electrons, which have been scattered through the surface quantum well via a diffraction process. The basic principle of photoelectron surface barrier interference is revealed by an analytical model. A quantitative comparison to the experiment is obtained by one-step photoemission calculations for different surface barrier models.