Picosecond pump-probe experiments on the C-O stretch vibration of acetic acid in solution with infrared pulses from a free-electron laser are presented. We show that under typical experimental conditions of pulses that are short compared to the inverse absorption linewidth and optically thick samples (necessary to observe significant transmission changes), the experimental pump-probe data are strongly influenced by pulse propagation effects (vibron polaritons) and coherent coupling between pump and probe vibron polaritons. To extract the vibrational lifetime from the data, it is therefore necessary to perform a full simulation of the propagation and coupling effects.