The association of peptides to phospholipid membranes through the insertion of an anchoring hydrocarbon tail is common to some viruses and to several anticancer drugs. We investigate the association of an anchor dipeptide, N-1740 myristoylated methyl glycine (MrG), to phospholipid membrane fragments made of 1-palmitoy1-2-linoleyl phosphatidylcholine (PLPC). Here we report on the experimental findings of 1620 two-dimensional infrared spectroscopy of an MrG backbone in E the 6 pm wavelength region. The experimental outcomes are supported by ab initio calculations and by a molecular dynamics simulation accomplished with the replica exchange method. We find that the guest molecule has a preferential unfolded conformation, with dihedral angles Phi = -90 +/- 20 degrees and Psi = -180 +/- 20 degrees, while the average orientational distribution of the amide I transition dipole moments with respect to the neighbor PLPC carbonyls is peaked at angles in the range 21-33 degrees. The depth of penetration of MrG inside the membrane corresponds rather well to the one estimated in our previous paper [J. Phys. Chem. B, 2009, 113, 16246], where we found that the backbone moieties of MrG are localized slightly above the carbonyl groups of PLPC. According to the simulation results, the anchor tail is completely inserted in the hydrophobic region of the bilayer, with a largely prevalent extended conformation and a preferential alignment along the average direction of the PLPC hydrocarbon tails.