PDS 70 hosts two massive, still-accreting planets and the inclined orientation of its protoplanetary disk presents a unique opportunity to directly probe the vertical gas structure of a planet-hosting disk. Here, we use high-spatial-resolution (≈0.″1; 10 au) observations in a set of CO isotopologue lines and HCO+ J = 4−3 to map the full 2D (r, z) disk structure from the disk atmosphere, as traced by 12CO, to closer to the midplane, as probed by less abundant isotopologues and HCO+. In the PDS 70 disk, 12CO traces a height of z/r ≈ 0.3, 13CO is found at z/r ≈ 0.1, and C18O originates at, or near, the midplane. The HCO+ surface arises from z/r ≈ 0.2 and is one of the few non-CO emission surfaces constrained with high-fidelity in disks to date. In the 12CO J = 3−2 line, we resolve a vertical dip and steep rise in height at the cavity wall, making PDS 70 the first transition disk where this effect is directly seen in line-emitting heights. In the outer disk, the CO emission heights of PDS 70 appear typical for its stellar mass and disk size and are not substantially altered by the two inner embedded planets. By combining CO isotopologue and HCO+ lines, we derive the 2D gas temperature structure and estimate a midplane CO snowline of ≈ 56–85 au. This implies that both PDS 70b and 70c are located interior to the CO snowline and are likely accreting gas with a high C/O ratio of ≈ 1.0, which provides context for future planetary atmospheric measurements from, e.g., JWST, and for properly modeling their formation histories.