For a laser driven molecule, we show that the ionization and the dissociation channels can be separated by preparing the molecule in a specific vibrational state. Specifically, we investigate the dynamics of the hydrogen molecular ion under a femtosecond infrared laser field aligned with the molecular axis. We find dissociation probabilities of more than 60%, considerably higher than reported so far. We demonstrate that a full dimensional description of the electron dynamics is necessary to obtain accurate results for the combined ionization/dissociation dynamics.