A theoretical study of two-photon ionization of H2 by low-intensity ultrashort xuv laser pulses is reported. The method is based on the solution of the time-dependent Schrodinger equation in a basis of stationary molecular vibronic states which include all electronic and vibrational degrees of freedom. In contrast with previous work, the doubly excited states, which also contribute to the ionization probabilities through autoionization, are explicitly included. We have found that, just below the one-photon ionization threshold, molecular autoionization leads to an enhancement of dissociative ionization, whose corresponding probability can be an order of magnitude larger than that of the nondissociative ionization process, and even larger than the corresponding dissociative probability in the one-photon absorption region. This result suggests that multicoincidence experiments, in which the orientation of the molecule with respect to the polarization axis is determined, might be easier to perform in the two-photon absorption regime than in the one-photon absorption regime. Electron angular distributions in the same range of photon energies are also reported.