(Au, Pt)/HfO₂/SiO₂/n-Si(001) metal-oxide-semiconductor structures with a thin (≈0.5 nm) SiO₂ layer, which is formed between HfO₂ and Si during atomic layer deposition of oxide layers, have been investigated via ballistic electron emission spectroscopy. The potential barrier heights at the (Au, Pt)/HfO₂ interfaces have been determined experimentally. The peculiarities observed in the curves of dependence of the collector current on the voltage between a scanning tunneling microscope probe and a metallic electrode are related to electron transport through the vacancy defect region of HfO₂ and the quantum-mechanical interference of electron waves arising from multiple reflections at the interfaces of the two-layer dielectric and at the interfaces of dielectric with a substrate and a metallic electrode.