We investigated the phase behavior and the microscopic structure of the colloidal complexes constituted from neutral/polyelectrolyte diblock copolymers and oppositely charged surfactant by dynamic light scattering (DLS) and small-angle neutron scattering (SANS). The neutral block is poly(N-isopropylacrylamide) (PNIPAM), and the polyelectrolyte block is negatively charged poly(acrylic acid) (PAA). In aqueous solution with neutral pH, PAA behaves as a weak polyelectrolyte, whereas PNIPAM is neutral and in good-solvent condition at ambient temperature, but in poor-solvent condition above similar to 32 degrees C. This block copolymer, PNIPAM-b-PAA with a narrow polydispersity, is studied in aqueous solution with an anionic surfactant, dodecyltrimethylammonium bromide (DTAB). For a low surfactant-to-polymer charge ratio Z lower than the critical value Z(C), the colloidal complexes are single DTAB micelles dressed by a few PNIPAM-b-PAA. Above Z(C), the colloidal complexes form a core-shell microstructure. The core of the complex consists of densely packed DTA(+) micelles, most likely connected between them by PAA blocks. The intermicellar distance of the DTA(+) micelles is similar to 39 angstrom, which is independent of the charge ratio Z as well as the temperature. The corona of the complex is constituted from the thermosensitive PNIPAM. At lower temperature the macroscopic phase separation is hindered by the swollen PNIPAM chains. Above the critical temperature T-C, the PNIPAM corona collapses leading to hydrophobic aggregates of the colloidal complexes.