We investigate the above-threshold multiphoton ionization of H_{2} embedded in superfluid He nanodroplets driven by ultraviolet femtosecond laser pulses. We find that the surrounding He atoms enhance the dissociation of in-droplet H_{2}^{+} from lower vibrational states as compared to that of isolated gas-phase molecules. As a result, the discrete peaks in the photoelectron energy spectrum correlated with the HHe^{+} from the dissociative in-droplet molecule shift to higher energies. Based on the electron-nuclear correlation, the photoelectrons with higher energies are correlated to the nuclei of the low-vibrationally excited molecular ion as the nuclei share less photon energy. Our time-dependent nuclear wave packet quantum simulation using a simplified He-H_{2}^{+} system confirms the joint contribution of the driving laser field and the neighboring He atoms to the dissociation dynamics of the solute molecular ion. The results strengthen our understanding of the role of the environment on light-induced ultrafast dynamics of molecules.