We report ab initio calculations on laser-assisted photoionization of the hydrogen molecule in the energy region where autoionization from doubly excited states is expected to occur. We use a UV-pump/IR-probe scheme in which an isolated attosecond UV pulse and a 750 nm IR pulse are combined. The IR pulse has a relatively low intensity (1012 W cm−2), which allows us to perform a perturbative analysis of the calculated ionization probabilities differential in either electron or nuclear energy or both. We show that, for dissociative ionization, the electron energy distributions as a function of time delay exhibit unusual streaking patterns that are due to the presence of autoionizing states. These patterns significantly differ from the standard ones observed in direct single ionization of atoms and molecules. We also show that, by using such a pump–probe scheme, one can suppress autoionization from doubly excited states for time delays between 0 and 4 fs.