We describe a new approach to calculate the binding of flexible peptides and unfolded proteins to multicomponent lipid membranes. The method is based on the transfer matrix formalism of statistical mechanics recently described as a systematic tool to study DNA-protein-drug binding in gene regulation. Using the energies of interaction of the individual polymer segments with different membrane lipid species and the scaling corrections due to polymer looping, we calculate polymer adsorption characteristics and the degree of sequestration of specific membrane lipids. The method is applied to the effector domain of the MARCKS (myristoylated alanine rich C kinase substrate) protein known to be involved in signal transduction through membrane binding. The calculated binding constants of the MARCKS(151-175) peptide and a series of related peptides to mixed PC/PS/PIP2 membranes are in satisfactory agreement with in vitro experiments.