The ionization and the dissociation of the diatomic molecular ion H 2 + have been investigated within a scheme where a noise field is added to an intense infrared laser field. The results show that both the ionization and the dissociation probabilities are enhanced with the introduction of the additional noise (the Gaussian white noise or the color noise) field. Further, by tuning the noise intensity and the delay time between the laser and the noise, a stochastic resonancelike curve is observed for the ionization or the dissociation dynamics, showing the existence of an optimal noise intensity and delay time for the given laser field.