2MASS K_S band data of the inner 60 pc of the Galaxy are used to reconstruct the line-of-sight distances of the giant molecular clouds located in this region. Using the 2MASS H band image of the same region, two different populations of point sources are identified according to their flux ratio in the two bands. The population of blue point sources forms a homogeneous foreground that has to be subtracted before analyzing the K_S band image. The reconstruction is made using two basic assumptions: (i) an axis-symmetric stellar distribution in the region of interest and (ii) optically thick clouds with an area filling factor of 1 that block all light of stars located behind them. Due to the reconstruction method, the relative distance between the different cloud complexes is a robust result, whereas it is not excluded that the absolute distance with respect to Sgr A* of structures located more than 10 pc in front of Sgr A* are understimated by up to a factor of 2. It is shown that all structures observed in the 1.2 mm continuum and in the CS(2-1) line are present in absorption. We place the 50 km s-1 cloud complex close to, but in front of, Sgr A*. The 20 km s-1 cloud complex is located in front of the 50 km s-1 cloud complex and has a large LOS distance gradient along the direction of the galactic longitude. The bulk of the Circumnuclear Disk is not seen in absorption. This leads to an upper limit of the cloud sizes within the Circumnuclear Disk of 0.06 pc.