The Spitzer Survey of Stellar Structure in Galaxies (S(4)G) is the largest available database of deep, homogeneous middle-infrared (mid-IR) images of galaxies of all types. The survey, which includes 2352 nearby galaxies, reveals galaxy morphology only minimally affected by interstellar extinction. This paper presents an atlas and classifications of S(4)G galaxies in the Comprehensive de Vaucouleurs revised Hubble-Sandage (CVRHS) system. The CVRHS system follows the precepts of classical de Vaucouleurs morphology, modified to include recognition of other features such as inner, outer, and nuclear lenses, nuclear rings, bars, and disks, spheroidal galaxies, X patterns and box/peanut structures, OLR subclass outer rings and pseudorings, bar ansae and barlenses, parallel sequence latetypes, thick disks, and embedded disks in 3D early-type systems. We show that our CVRHS classifications are internally consistent, and that nearly half of the S(4)G sample consists of extreme late-type systems (mostly bulgeless, pure disk galaxies) in the range Scd-Im. The most common family classification for mid-IR types S0/a to Sc is SA while that for types Scd to Sm is SB. The bars in these two type domains are very different in mid-IR structure and morphology. This paper examines the bar, ring, and type classification fractions in the sample, and also includes several montages of images highlighting the various kinds of "stellar structures" seen in mid-IR galaxy morphology.