We investigate the capacity of extracting near-surface shear-wave velocity by considering dispersive surface waves and non-dispersive reflected waves. We show that indeed the full waveform fitting of these waves requires a dedicated approach by using lateral spatial and frequential coherence for surface waves and by explicitely introduces the fitting of reflected waves in the inversion formulation. On a simple example as a two-layers model, lateral variations of the velocity are reconstructed while the low-wavenumber content of the velocity could be improved through reflection waves. Combining these two sources of information on the shear-wave velocity could improve our shear-wave velocity imaging in the near-surface context.