Photoionization of molecular species is, essentially, a multipath interferometer with both experimentally controllable and intrinsic molecular characteristics. In this work, XUV photoionization of impulsively aligned molecular targets (N_{2}) is used to provide a time-domain route to "complete" photoionization experiments, in which the rotational wave packet controls the geometric part of the photoionization interferometer. The data obtained is sufficient to determine the magnitudes and phases of the ionization matrix elements for all observed channels, and to reconstruct molecular frame interferograms from lab frame measurements. In principle, this methodology provides a time-domain route to complete photoionization experiments and the molecular frame, which is generally applicable to any molecule (no prerequisites), for all energies and ionization channels.