We report results of a multi-wavelength study of interstellar absorption in diffuse molecular clouds that lie in the direction of flat-spectrum quasars. Quasars as back-ground sources allow the measurement of Galactic interstellar absorption across the electromagnetic spectrum from mm to X-ray wavelengths. We have obtained high-resolution (≈3 km s-1) near-UV to far-red spectra (3300-10400 \uc5) of nine quasars as well as several Galactic sources with the UV-Visual Echelle Spectrograph (UVES) at the Very Large Telescope (VLT) UT2 of the European Southern Observatory (ESO). This is the first optical study of the classical molecules CH and CH+ along the same lines of sight used for mm absorption studies of polyatomic molecules like HCO+, C2H, and H2CO, which have been observed by H.S. Liszt and R. Lucas at unexpectedly high abundances in diffuse molecular gas. For the quasars PKS 0736+017 and PKS 2251+158 we see CH absorption at the same velocities as HCO+ observed at mm wavelengths. The CH and CH+ lines are also connected to distinct Galactic absorption components of Ca II, Na I, and K I that we see in our spectra. We also used the data obtained for this project to study redshifted emission and absorption lines originating in the AGN and from intervening absorption systems. We present a detailed study of the zabs=0.79 metal-rich intervening absorber toward PKS 2145+067. One of the Galactic background sources of our project is the pulsar of the Crab Nebula supernova remnant. We show the the first spectra of high spatial (sub-arcsecond) and spectral (≈3 km s-1) resolution of the material within 10\u27 of the Crab pulsar. We detect a host of nebular emission lines, including [O II], [O III], [S II], [S III], H β/γ, He I, He II, [C I], [Ne III], [Ar III], and [Ni II], at kinematic heliocentric velocities ranging from about +1500 to -1200 km s-1
