We demonstrate that time-domain ptychography, when applied to a set of broadband vibrational sum frequency spectra, reconstructs amplitude and phase of the vibrational free induction decay from an interfacial sample with a resolution that is independent of up-converting pulse bandwidth and spectrometer resolution. These important improvements require no modifications to most standard homodyne setups, and the method is applicable to other coherent homodyne spectroscopies such as coherent anti-Stokes Raman spectroscopy and transient grating spectroscopy.