We present a broadband vibrational sum frequency generation (BB-VSFG) scheme using a novel ps visible pulse shape. We generate the fs IR pulse via standard procedures and simultaneously generate an 'inverted' time-asymmetric narrowband ps visible pulse via second harmonic generation in the pump depletion regime using a very long nonlinear crystal which has high group velocity mismatch (LiNbO3). The 'inverted' ps pulse shape minimally samples the instantaneous nonresonant response but maximally samples the resonant response, maintaining high spectral resolution. We experimentally demonstrate this scheme, presenting SFG spectra of canonical organic monolayer systems in the C-H stretch region (2800-3000 cm(-1)).