Photoexcitation induces intricate changes in both the real and imaginary components of the complex refractive index of thin film materials, which is essential for interpreting transient spectral features. Here, we employ a Kramers-Kronig-based analytical approach to elucidate light-induced changes in the complex refractive index from transient transmission spectra of thin films. Using gold-perovskite films as model systems, we conduct experimental measurements of transient transmission spectra for both individual gold and perovskite films, as well as for the bilayer heterostructure. Our analysis reveals significant changes in the refractive index and absorption for these systems. Notably, we observe negligible photocarrier transfer between the gold and perovskite layers based on transient spectroscopic analysis. These findings have implications for the design and optimization of bilayer heterostructures in optoelectronic applications. This work highlights the importance of spectroscopic techniques in studying the photophysical properties of heterostructure films.