We have studied the optical properties of four (LaNiO3)n/(LaMnO3)2 superlattices (SL) (n=2,3,4,5) on SrTiO3 substrates. We have measured the reflectivity at temperatures from 20 to 400 K, and extracted the optical conductivity through a fitting procedure based on a Kramers-Kronig consistent Lorentz-Drude model. With increasing LaNiO3 thickness, the SLs undergo an insulator-to-metal transition (IMT) that is accompanied by the transfer of spectral weight from high to low frequency. The presence of a broad midinfrared band, however, shows that the optical conductivity of the (LaNiO3)n/(LaMnO3)2 SLs is not a linear combination of the LaMnO_{3} and LaNiO3 conductivities. Our observations suggest that interfacial charge transfer leads to an IMT due to a change in valence at the Mn and Ni sites.