  Elucidating the interplay between nuclear and electronic degrees of freedom
that govern the complex dielectric behavior of materials under intense
photoexcitation is essential for tailoring optical properties on demand.
However, conventional transient reflectivity experiments have been unable to
differentiate between real and imaginary components of the dielectric response,
omitting crucial electron-lattice interactions. Utilizing thin film
interference we unambiguously determined the photoinduced change in complex
dielectric function in the Peierls semimetal bismuth and examined its
dependence on the excitation density and nuclear motion of the A$_{1g}$ phonon.
Our modeled transient reflectivity data reveals a progressive broadening and
redshift of Lorentz oscillators with increasing excitation density and
underscores the importance of both, electronic and nuclear coordinates in the
renormalization of interband transitions.
