We investigate the turbulent transport of a passive scalar in turbulent flows between a flat top wall and two different complex surfaces and describe the influence of the different surface geometries on the mixing properties. In order to achieve a homogeneous and inhomogeneous reference flow situation two different types of surface geometries are considered: (i) a sinusoidal bottom wall profile with an amplitude-to-wavelength ratio of α=2a/Λ=0.1 (Λ=30mm); and (ii) a profile consisting of two superimposed sinusoidal waves with α=2a/Λ=0.1 (Λ=30mm). The laboratory investigations were performed by use of a combined digital particle image velocimetry (DPIV) and planar laser induced fluorescence (PLIF) technique to examine the spatial variation of the streamwise, spanwise and wall-normal velocity components, and to assess the concentration field of the scalar. Long image sequences (frame rate 4 Hz) are obtained from both DPIV and PLIF to calculate time-averaged statistics of the velocity field and the scalar field. We discuss the influence of the complex surfaces on the scalar transport. A higher spanwise spreading of the scalar plume is observed compared to plane channel flows. Due to the influence of the complex surface there is at first a higher transport normal to the mean flow direction and at second there is no complete "smoothing" of the instantaneous structures in the mean scalar field as it is the case in a similar source configuration in a plane channel flow. The mixing properties of the turbulent flow are enhanced for the surface composed of two superimposed waves compared to the sinusoidal wavy surface.