Infrared spectroscopic ellipsometry (IRSE) is a powerful optical probe of various chemical and physical properties of molecules adsorbed onto solid surfaces. In particular, IRSE can be useful for detecting adsorption-induced changes in the IR spectra of self-assembled monolayers (SAMs), and unlike traditional IR absorption spectroscopies, IRSE provides useful information about the phase of the reflected radiation from the SAMs. However, in the standard IRSE experimental geometry using flat substrates for SAMs, the detectable signal containing these phase data is considerably weaker than the corresponding absorbance data. In our present work, we demonstrate that enhancing the local optical fields at the sample surface through the use of a disordered Au nanoisland substrate can substantially increase both these absorbance and phase signals. We also demonstrate how this surface-enhanced infrared spectroscopic ellipsometry (SEIRSE) can be utilized for straightforward analysis of absorption peak widths, as well as to obtain information about the orientation of the terminal methyl on adsorbed SAMs. As model SAMs for this study, we use undecanethiol (UDT) containing 10 CH2 units and a terminal CH3 group, as well as dodecanethiol (DDT) containing 11 CH2 units with its terminal CH3 at a different orientation than UDT. We show that surface-enhanced IRSE is sensitive to subtle vibrational signatures of the differently oriented terminal methyls of these two homologous alkanethiol SAMs.