We have used archival far-ultraviolet spectra from observations made by HST STIS and FUSE to determine the column densities and rotational excitation temperatures for carbon monoxide and molecular hydrogen, respectively, along 23 sight lines to Galactic O and B stars. The reddening values range from E(B - V) = 0.07 to 0.62, sampling the diffuse to translucent interstellar medium (ISM). We find that the H₂ column densities range from 5 × 10¹⁸ to 8 × 10²⁰ cm^-2 and the CO from upper limits around 2 × 10¹² cm^-2 to detections as high as 1.4 × 10¹⁶ cm^-2. CO increases with increasing H₂, roughly following a power law of factor ~2. The CO/H₂ column density ratio is thus not constant, ranging from 10^-7 to 10^-5, with a mean value of 3 × 10^-6. The sample segregates into "diffuse" and "translucent" regimes, the former with molecular fraction 0.25 and A_V/d < 1 mag kpc^-1. The mean CO/H₂ for these two regimes are 3.6 × 10^-7 and 9.3 × 10^-6, respectively, significantly lower than the canonical dark cloud value of 10^-4. Six sight lines show the isotopic variant ¹³CO, and the isotopic ratio we observe (~50-70) is consistent with, if perhaps a little below, the average ¹²C/¹³C for the ISM at large. The average H₂ rotational excitation temperature is 74 ± 24 K, agreeing well with previous studies, and the average CO temperature is 4.1 K, with some sight lines showing temperatures as high as 6.4 K. The higher excitation CO is observed with higher column densities, consistent with the effects of photon trapping in clouds with densities in the 20-100 cm^-3 range. We discuss the implications for the structure of the diffuse/translucent regimes of the ISM and the estimation of molecular mass in galaxies.