Phase-sensitive sum-frequency spectroscopy is a unique tool to interrogate the vibrational structure of interfaces. A precise understanding of the interfacial structure often relies on accurately determining the phase of χ(2), which has recently been demonstrated using a nonlinear interferometer in conjunction with a frequency-scanning picosecond laser system. Here, we implement nonlinear interferometry using a femtosecond laser system for broadband sum-frequency generation. The phase of the vibrational response from a self-assembled monolayer of octadecanethiol on gold is determined using the nonlinear femtosecond interferometer. The results are compared to those obtained using the more traditional heterodyne-detected phase measurements. Both methods give a similar phase spectrum and phase uncertainty. We also discuss the origin of the phase uncertainties and provide guidelines for further improvement.