Turbulence measurements for a zero pressure gradient boundary layer over a two-dimensional roughness are presented and compared to previous results for a smooth wall and a three-dimensional roughness (Volino, Schultz & Flack, J. Fluid Mech., vol. 592, 2007, p. 263). The present experiments were made on transverse square bars in the fully rough flow regime. The turbulence structure was documented through the fluctuating velocity components, two-point correlations of the fluctuating velocity and swirl strength and linear stochastic estimation conditioned on the swirl and Reynolds shear stress. The two-dimensional bars lead to significant changes in the turbulence in the outer flow. Reynolds stresses, particularly and , increase, although the mean flow is not as significantly affected. Large-scale turbulent motions originating at the wall lead to increased spatial scales in the outer flow. The dominant feature of the outer flow, however, remains hairpin vortex packets which have similar inclination angles for all wall conditions. The differences between boundary layers over two-dimensional and three-dimensional roughness are attributable to the scales of the motion induced by each type of roughness. This study has shown three-dimensional roughness produces turbulence scales of the order of the roughness height k while the motions generated by two-dimensional roughness may be much larger due to the width of the roughness elements. It is also noted that there are fundamental differences in the response of internal and external flows to strong wall perturbations, with internal flows being less sensitive to roughness effects.