We have predicted using computer simulations and have detected with SAXS measurements that pH-sensitive core-shell polyampholyte microgels can form a dense layer ("skin") at the core-shell interface. The microgels have cationic core and neutral shell at low pH, whereas the core becomes neutral and the shell becomes anionic at high pH. The core and shell are oppositely charged at intermediate pH values. The layer formation is a result of the electrostatic complexation between oppositely charged subchains. We have studied microgels with different core-shell ratios and fractions of ionizable groups and analyzed radial distribution of polymer volume fraction and volume fractions of cationic and anionic groups. We have demonstrated that in many cases complexation of oppositely charged subchains (intermediate pH values) or swelling of charged core with neutral shell (low pH) are responsible for the formation of quasi-hollow structures with a loose core of strongly swollen subchains and dense shell of interpenetrating core- and shell-forming subchains. The most pronounced quasi-hollow structures are predicted in computer simulations for highly charged microgels. On the contrary, practically homogeneous swelling of the microgels is observed at high pH, when electrostatics-driven swelling of the anionic shell promotes swelling of the neutral core. All structures are colloidally stable due to the spatial segregation of the opposite charges. Therefore, the microgels can be useful as carriers for pH-controlled uptake, storage, and release of neutral guest molecules, which can be trapped within the microgel at low and intermediate pH and released at high pH.