Polystyrene sulfonate (PSS 77 kDa) adsorbed onto oppositely charged dioctadecyldimethylammonium bromide (DODA) monolayers at the air/water interface is investigated with X-ray reflectivity and grazing incidence diffraction. The alkyl tails of DODA in the condensed phase form an oblique lattice with large tilts and intermediate azimuth angle. On PSS adsorption, the alkyl tail structure is maintained; only the tilt angle changes. Bragg peaks caused by flatly adsorbed, aligned PSS chains are observed, when DODA is in the fluid and also when it is in the condensed phase. The two-dimensional lamellar phase is only found at intermediate PSS bulk concentrations (0.001-1 mmol/L). In this phase, the PSS coverage can be varied by a factor of 3, depending on DODA molecular area and polymer bulk concentration. Charge compensation in the lamellar phase is almost achieved at 1 mmol/L. At larger bulk concentrations, PSS adsorbs flatly yet without chain alignment. Presumably, a necessary condition for a two-dimensional lamellar phase is a pronounced electrostatic force which causes a large persistence length as well as repulsion between the aligned chains.