A sample of 379 extragalactic sources is presented that has mid-infrared, high-resolution spectroscopy from the Spitzer Infrared Spectrograph (IRS) and also spectroscopy of the [CII]158{mu}m line from the Herschel Photodetector Array Camera and Spectrometer (PACS). The emission line profiles of [NeII]12.81{mu}m, [NeIII]15.55{mu}m, and [CII]158{mu}m are presented, and intrinsic line widths are determined (full width half maximum of Gaussian profiles after instrumental correction). All line profiles, together with overlays comparing the positions of PACS and IRS observations, are made available in the Cornell Atlas of Spitzer IRS Sources (CASSIS). Sources are classified from active galactic nucleus (AGN) to starburst based on equivalent widths of the 6.2{mu}m polycyclic aromatic hydrocarbon feature. It is found that intrinsic line widths do not change among classifications for [CII], with median widths of 207km/s for AGNs, 248km/s for composites, and 233km/s for starbursts. The [NeII] line widths also do not change with classification, but [NeIII] lines are progressively broader from starburst to AGN. A few objects with unusually broad lines or unusual redshift differences in any feature are identified.