We explore a novel method to obtain scattering and absorption (S&A) coefficients of inhomogeneous materials from measurements of regular transmittance and specular reflectance. We use a Spectral Projected Gradient Method (SPGM) to invert experimental spectra. The SPGM method requires an initial approximation to the S&A coefficients, which is needed to ensure convergence to an optimized solution. We discuss problems associated with multiple solutions and conditions for the obtained optimal solution to be a good approximation to the physical one. We present results for TiO₂/polyvinylpyrrolidone (PVP)-water, plasmonic Au/PVP-water and ferromagnetic Fe₃O₄/PVP-water materials. The obtained S&A coefficients indicate that these materials are dilute suspensions of dense particle clusters in the dependent scattering regime. We argue that the SPGM gives physically realistic solutions for this class of materials. The SPGM has the advantages that it is much less expensive in computational terms and easier to implement than previously used simulated annealing methods.