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We use angle resolved photoemission spectroscopy to investigate the coupling of electron quantum well states (QWSs) in epitaxial thin Pb and Ag films. More specifically, we investigate the Ag/Si, Pb/Si, and Pb/Ag/Si systems. We found that the parallel momentum plays a very profound role in determining how two adjacent quantum wells are coupled electronically across the interface. We revealed that in the Pb/Ag bimetallic system, there exist two distinctly different regimes in the energy vs momentum (E vs k) space. In one regime, the electronic states in Ag and Pb are strongly coupled, resulting in a new set of QWSs for the bi-metallic system. In the other regime, the electronic states in individual metallic layers are retained in their respective regions, as if they are totally decoupled. This result is corroborated by calculations using density functional theory. We further unravel the underlying mechanism associated with the electron refraction and total internal reflection across the interface.