Precise engineering of phonon-phonon (ph-ph) and electron-phonon (e-ph) interactions by materials design is essential for an in-depth understanding of thermal, electrical, and optical phenomena as well as new technology breakthrough governed by fundamental physical laws. Due to their characteristic length scale, the ph-ph and e-ph interactions can be dramatically modified by nanoscale spatial confinement, thus opening up opportunities to finely maneuver underlying coupling processes through the interplay of confined size, fundamental length scale, and interface. We have combined ultrafast optical spectroscopy with a series of well-designed nanoscale core-shell structures possessing precisely tunable interface to demonstrate for the first time unambiguous experimental evidence of coherent interfacial phonon coupling between the core and shell constituents. Such interfacially coupled phonons can be impulsively excited through the e-ph interaction, in which the critical e-ph coupling constant is further shown to be monotonically controlled by tuning the configuration and constituent of core-shell nanostructure. Precise tunability of elemental physics processes through nanoscale materials engineering should not only offer fundamental insights into different materials properties but also facilitate design of devices possessing desirable functionality and property with rationally tailored nanostructures as building blocks.