The south polar layered deposits of Mars contain a massive CO2 ice reservoir formed during periods of low planetary obliquity and partial atmospheric collapse. Within the reservoir are bounding layers (BLs) that are believed to consist entirely of water ice and modify CO2 ice stability during periods of higher obliquity and insolation. Here we use three-dimensional data from the Shallow Radar instrument to extend and update past mapping efforts of the reservoir in order to evaluate its internal structure and mass distribution. By mapping the entirety of each BL as two distinct reflectors, we provide individual volumetric calculations of the multiple CO2 units for the first time (146, 1,472, and 5,493 km(3)) and discover a new, smaller unit (12 km(3)). Our volumetric measurements provide critical parameters to understanding past climatic states and climatological modeling, including the magnitude of atmospheric collapse and rebound over three separate events. We also provide updated thickness and areal extent measurements of BL1 (31 +/- 5 m, 1,001 km(2)), BL2 (32 +/- 9 m, 5,415 km(2)) and BL2+3 (42 +/- 12 m, 4,232 km(2)), with maximum thickness of similar to 80 m. By mapping the entirety of the BLs, we find novel radar observations, attainable only in 3D, which support previous interpretations that both BL are composed of water ice. Our novel measurements will support climatological studies of Mars' atmosphere in the past 500 kyr. Plain Language Summary The massive carbon dioxide (CO2) ice deposits beneath the surface of Mars' south pole are separated by layers of water (H2O) ice called bounding layers. The CO2 deposits formed from the freezing of atmospheric CO2 during colder periods on Mars, and the water ice layers that separate them represent periods of sublimation. The remaining CO2 provides indication for the magnitude of partial atmospheric collapse in a sequence of historical events dating back similar to 500,000 years. Using radar sounding data, we measure the thickness, extent, and volume of each of these alternating units of H2O ice and CO2 ice in their entirety, giving a more precise determination of those atmospheric collapses for the first time. We also identify important features within the deposits that support the interpretation that the bounding layers are composed of H2O ice. Our measurements of all of the units provide critical input parameters for climate models of Mars' past. Because the formation of these deposits depends on historical temperature cycles, constraining these parameters in climate models already provides a better view of how Mars' atmosphere has evolved.