In the present work, we presented an analysis of the unusual recognition specificity exhibited by marked difference in the binding behavior of dipeptide with amphiphilic head group when subtle relative change of N-terminal and C-terminal of the dipeptide are made. Recently, in a series of detailed experiments, binding of aqueous dipeptides, GlyX and X/Gly (X = Leu, Phe, Pro, Ala; X/ = Leu, Phe) with dialkyl oligoglycyl amphiphiles is studied [X. Cha, K. Ariga, M. Onda, and T. Kunitake, J. Am. Chem. Soc. 117, 11833 (1995)]. It is observed that GlyX are specifically bound to 2C18BGly2NH2 while X/Gly are insignificantly bound. We first studied the conformational energy variation of GlyPhe, PheGly and model of 2C18BGly2NH2 amphiphile using semi-empirical and ab-initio methods in vacuum. Using the individual energy optimized monomer structure of amphiphile and peptide, we studied the binding energy of optimized GlyPhe: amphiphile pair and PheGly: amphiphile pair structures at 1:1 and 1:2 ratio at the same level of theory using a population of structures. Binding of GlyPhe is favorable over the binding of PheGly at various levels of theory (semi-empirical and ab-initio). It is noted that the hydrogen bonding pattern in the GlyPhe binding is more effective than that in the PheGly binding. In the population of low energy structures, PheGly: amphiphile structures have more exposed area around the hydrophobic Phe group than the GlyPhe: amphiphile structures. Relatively more PheGly: amphiphile structures have intermolecular orientation unsuitable to contribute to the population of head group structures relevant in aqueous interface. Summarizing, significantly better binding capacity of GlyPhe over the PheGly with amphiphile, is due to the difference in hydrogen bonding interaction pattern, hydrophobic effect and possible orientations of the amphiphile and peptide at interface, relevant to the condensed phase monolayer structure. All the three factors cooperatively lead to favorable recognition of GlyPhe over PheGly as observed in experiment. A calculation of the ratio of the amphiphile-peptide bound complex to the initial concentration of the amphiphile indicates that the diffusional process at the peptide interfaces could be significantly influenced by hydrogen bonding.