IUE spectra of Herbig-Haro object 2H are presented. The spectra show a strong 'excess' UV continuum and prominent emission lines of C, N, O, Si, Mg, and possibly Al. The continuum, F(lambda), exhibits a turnover shortward of about 1450 A, confirming for the first time the H0 two-photon nature of the emission source. A possible absorption feature near 1680 A, which could result from a new grain or molecular constituent in these protostellar objects is also noted. Recently computed models of steady shocks into partially ionized gas reproduce the two-photon spectral shape, but its observed intensity relative to H-beta and the Balmer continuum is anomalously high. It is suggested that a range of shock velocities, 70-100 km/s, or nonsteady, 'truncated' shocks may be responsible. Future high-sensitivity UV observations of HH objects may be used to probe grain extinction curves in star-forming regions.