We calculate the free energy surfaces for two small proteins and a protein-RNA complex system by using a lattice model approach. In particular, we employ the Munoz-Eaton model, which is a native-structure based statistical mechanical model for studying protein folding problem. The model can provide very useful insights into the folding mechanisms by allowing one to calculate the free energy surfaces efficiently. We first calculate the free energy surfaces of ubiquitin and BBL, using both approximate and recently developed exact solutions of the model. Ubiquitin exhibits a typical two-state folding behavior, while BBL downhill folding in our study. We then extend the method to study of a protein-RNA complex. In particular, we focus on PAZ-siRNA complex. In order to elucidate the interplay between folding and binding kinetics for this system we perform comparative studies of PAZ only, PAZ-siRNA complex and two mutated complexes. We find that folding and binding are strongly coupled with each other and the bound PAZ is more stable than the unbound PAZ. Our results also suggest that the binding sites of the siRNA may serve act as a nucleus in the folding process.