We present free energy calculations on a set of complexes of antimicrobial peptides and SDS/DPC micelles. DPC (dodecyl phosphatidylcholine) and SDS (Sodium dodecyl sulphate) micelles resemble zwitterionic mammalian lipid and anionic bacterial membrane interfaces, respectively. Equilibrium structures of the peptides, micelles and peptide-micelle complexes are obtained from snapshots taken from up to 40 ns molecular dynamics simulations. A thermodynamic cycle is introduced to decompose the binding free energy into electrostatic, non-electrostatic and entropic contributions. The electrostatic solvation energies of each peptide, micelle and peptide-micelle complex are calculated using Poisson-Boltzmann and Generalized Born models averaged over multiple conformations. The nonpolar contributions to the free energy are approximated using a linear solvent-accessible surface area relationship. The entropic part of the free energy is decomposed into translational, rotational, conformational and vibrational contributions. Translational and rotational entropies are computed by utilizing polyatomic ideal gas formulas. Peptide conformational entropy is obtained using the empirical scale of Pickett and Sternberg while vibrational entropy is calculated using normal modes frequencies. Although it is difficult to compute absolute binding free energies, relative binding free energy calculations are shown to reproduce the experimentally observed rankings for peptide antimicrobial activities and hemolytic toxicities. Finally, these calculations have the potential of screening mutant peptides for high antimicrobial activity as well as low hemolytic toxicity, and thereby optimizing therapeutic efficiency.