We present the results of a Doppler tomographic reconstruction of the UV spectra of the double-lined, O binary DH Cephei based on observations made with the International Ultraviolet Explorer. We describe cross-correlation methods we use to obtain precise radial velocities, and we present a radial velocity curve based on combined optical and UV measurements. We also show how we use fits of the cross-correlation functions to estimate the UV flux ratio and projected rotational velocities. The individual component spectra are classified as O6 V + O7 V using UV criteria defined by Penny, Gies, & Bagnuolo. We place the individual components in the theoretical Hertzsprung-Russell diagram using the distance modulus and reddening estimated for its home cluster, NGC 7380, and we find that the stars are larger than estimates from prior studies of the ''ellipsoidal'' light variations. We reconsider the ellipsoidal light curve and show that there is a range in acceptable stellar radii (as a function of orbital inclination). We discuss the constraints on inclination and system masses based on cluster distance modulus, presumed synchronous rotation, and on consistency with masses derived from evolutionary tracks (which involves the issue of the temperature calibration of O stars). We find that primary and secondary masses of 39-50 M. and 35-45 M., respectively, satisfy all the constraints from spectroscopy, photometry, distance modulus, and single-star evolutionary tracks.