In condensed matter, scattering processes determine the transport of charge carriers. In case of heterostructures, interfaces determine many dynamic properties such as charge transfer and transport, and spin current dynamics. Here, we discuss optically excited electron dynamics and their propagation across a lattice-matched, metal-metal interface of single crystal quality. Using femtosecond time-resolved linear photoelectron spectroscopy upon optically pumping different constituents of the heterostructure, we establish a technique that probes the electron propagation and its energy relaxation simultaneously. In our approach, a near-infrared pump pulse excites electrons directly either in the Au layer or in the Fe layer of epitaxial Au/Fe/MgO(001) heterostructures while the transient photoemission spectrum is measured by an ultraviolet probe pulse on the Au surface. Upon femtosecond laser excitation, we analyze the relative changes in the electron distribution close to the Fermi energy and assign characteristic features of the time-dependent electron distribution to transport of hot and nonthermalized electrons from the Fe layer to the Au surface and vice versa. From the measured transient electron distribution, we determine the excess energy, which we compare with a calculation based on the two-temperature model that takes diffusive electron transport into account. On this basis, we identify a transition with increasing Au layer thickness from a superdiffusive to a diffusive transport regime at 20–30 nm.