A laboratory search for coincidences of transitions between excited states in H2 with frequencies of diffuse interstellar bands (DIBs) was performed employing an XUV-Vis laser-based double-resonance scheme. Single quantum levels of various rovibrational states of the C 1Πu state of H2, populated by means of transitions at 86 nm, were used as intermediate states for the absorption of a visible photon. Although some coincidences are found, a recent hypothesis involving detailed assignments of DIBs to specific transitions in H2 is not confirmed. Spectral profiles are recorded that mimic characteristic triplet structures and asymmetric lineshapes as observed in DIBs. Based on the present findings the hypothesis of H2 as the carrier of diffuse interstellar bands is discussed from a more general perspective.