The Molecules with ALMA at Planet-forming Scales (MAPS) Large Program provides a unique opportunity to study the vertical distribution of gas, chemistry, and temperature in the protoplanetary disks around IM Lup, GM Aur, AS 209, HD 163296, and MWC 480. By using the asymmetry of molecular line emission relative to the disk major axis, we infer the emission height (z) above the midplane as a function of radius (r). Using this method, we measure emitting surfaces for a suite of CO isotopologues, HCN, and C2H. We find that (CO)-C-12 emission traces the most elevated regions with z/r> 0.3 <i , while emission from the less abundant (CO)-C-13 and (CO)-O-18 probes deeper into the disk at altitudes of z/r less than or similar to 0.2 <i . C2H and HCN have lower opacities and signal-to-noise ratios, making surface fitting more difficult, and could only be reliably constrained in AS 209, HD 163296, and MWC 480, with z/r less than or similar to 0.1 <i , i.e., relatively close to the planet-forming midplanes. We determine peak brightness temperatures of the optically thick CO isotopologues and use these to trace 2D disk temperature structures. Several CO temperature profiles and emission surfaces show dips in temperature or vertical height, some of which are associated with gaps and rings in line and/or continuum emission. These substructures may be due to local changes in CO column density, gas surface density, or gas temperatures, and detailed thermochemical models are necessary to better constrain their origins and relate the chemical compositions of elevated disk layers with those of planet-forming material in disk midplanes. This paper is part of the MAPS special issue of the Astrophysical Journal Supplement.