The effect of the refractive index mismatch on light propagation through diffusive layers has been investigated. The refractive index mismatch changes the balance of energy inside the medium determining a temporal and spatial redistribution of light. Light penetration through the medium is obstructed (facilitated) by a negative (positive) refractive index step variation. An analytical solution of the time-dependent diffusion equation that accounts for this effect has been obtained. The solution has been validated by comparisons with the results of Monte Carlo simulations. An excellent description of light propagation is given even for a high refractive index mismatch.