We measured the height of the chromospheric network in the 1700, 1600, and 304 A wavelength bands of the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) from the shift of features on the disk with respect to corresponding features in SDO/Helioseismic and Magnetic Imager (HMI) images of the absolute value of the longitudinal magnetic field. We found that near the limb the 304 A network emission forms 3.60$pm$0.24 Mm above the 1600 A emission, which, in turn, forms 0.48$pm$0.10 Mm above the HMI (6173 A) level. At the center of the disk the corresponding height differences are 2.99$pm$0.02 Mm and 0.39$pm$0.06 Mm respectively. We also found that the 1600 A network emission forms 0.25$pm$0.02 Mm above the 1700 A emission near the limb and 0.20$pm$0.02 Mm at the disk center. Finally, we examined possible variations with the solar cycle. Our results can help to check and refine atmospheric models.