Solid-state complexes of flexible polymers with surfactants (surf) exhibit mesomorphic phase and microphase-separated lamellar morphology. Because the surf molecules are strongly associated with the polymer backbone, the ordered packing of the alkyl tails should be cooperative with the chain packing in the polymer layers which is influenced by chain topology. In this study, the supramolecular structure and thermal properties of the complexes of a highly branched poly(ethylenimine) (PEI) with dodecyl-benzenesulfonic acid (DBSA) were investigated. Polarized optical microscopy and small-angle X-ray scattering (SAXS) revealed the presences of mesomorphic phases and microphase-separated lamellar morphology in the complexes. The ordered supramolecular structure was observed not only for the stoichiometric composition but over a wide composition range. The thicknesses of polymer and surf layers were determined from the one-dimensional correlation function. The surf layer thickness varied with complex composition. The glass transition temperature of polymer layers was raised by complexation because of the stiffening of polymer chains. Complexation with DBSA also enhanced the thermal stability of PEI, where the thermal decomposition temperature can be raised by as much as 50 degrees C.