We report the results of a survey at very high spectral resolution of interstellar CH and CH+ in diffuse clouds toward 20 bright stars, and medium-resolution observations to determine radial velocities. The high-resolution observations [(λ/δλ) ∼ 500,000] resolve all the CH+ and all the CH lines. Most of the CH lines show multiple overlapping components at this resolution. It is often possible to associate a weak broad CH component with a CH+ component of similar radial velocity and width. The implications of these results for CH and CH+ formation scenarios are discussed.