Engineering layer-layer interactions provides a powerful way to realize novel and designable quantum phenomena in van der Waals heterostructures(1-6). Interlayer electron-electron interactions, for example, have enabled fascinating physics that is difficult to achieve in a single material, such as the Hofstadter's butterfly in graphene/boron nitride (hBN) heterostructures(5-10). In addition to electron-electron interactions, interlayer electron-phonon interactions allow for further control of the physical properties of van der Waals heterostructures. Here we report an interlayer electron-phonon interaction in WSe2/hBN heterostructures, where optically silent hBN phonons emerge in Raman spectra with strong intensities through resonant coupling to WSe2 electronic transitions. Excitation spectroscopy reveals the double-resonance nature of such enhancement, and identifies the two resonant states to be the A exciton transition of monolayer WSe2 and a new hybrid state present only in WSe2/hBN heterostructures. The observation of an interlayer electron-phonon interaction could open up new ways to engineer electrons and phonons for device applications.