Based on diblock copolymers, a pair of "schizophrenic" micellar systems is designed by combining a nonionic and thermoresponsive block with a zwitterionic block, which is thermoresponsive and salt-sensitive. The nonionic block is poly(N-isopropylacrylamide) (PNIPAM) or poly(N-isopropylmethacrylamide) (PNIPMAM) and exhibits a lower critical solution temperature (LCST) behavior in aqueous solution. The zwitterionic block is a polysulfobetaine, i.e., poly(4((3-methacrylamidopropyl)dimethylammonio)butane-1-sulfonate) (PSBP), and has an upper critical solution temperature (UCST) behavior with the clearing point decreasing with increasing salt concentration. The PSBP-b-PNIPAM and PSBP-b-PNIPMAM diblock copolymers are prepared by successive reversible addition-fragmentation chain transfer (RAFT) polymerizations. The PSBP block is chosen such that the clearing point of the homopolymer is significantly higher in pure water than the cloud point of PNIPAM or PNIPMAM. Using turbidimetry, H-1 NMR, and small-angle neutron scattering, we investigate the overall phase behavior as well as the structure and interaction between the micelles and the intermediate phase, both in salt-free D2O and in 0.004 M NaBr in D2O in a wide temperature range. We find that PSBP-b-PNIPAM at 50 g L-1 in salt-free D2O is turbid in the entire temperature range. It forms spherical micelles below the cloud point of PNIPAM and cylindrical micelles above. Similar behavior is observed for PSBP-b-PNIPMAM at 50 g L-1 in salt-free D2O with a slight and smooth increase of the light transmission below the cloud point of PNIPMAM and an abrupt decrease above. Upon addition of 0.004 M NaBr, the UCST-type cloud point of the PSBP-block is notably decreased, and an intermediate regime is encountered below the cloud point of PNIPMAM, where the light transmission is slightly enhanced. In this regime, the polymer solution exhibits behavior typical for polyelectrolyte solutions. Thus, double thermosensitive and salt-sensitive behavior with "schizophrenic" micelle formation is found, and the width of the intermediate regime, where both blocks are hydrophilic, can be tuned by the addition of electrolyte.