The characteristics of turbulent jets interacting with a free surface were investigated experimentally. The experiments were performed to quantify the effects of offset height and nozzle geometry on the turbulent characteristics at low Reynolds number (Re = 5500). The offset height ratio of a square jet was varied from 1 to 4. For the nozzle geometry effect, four nozzle configurations including circular, square, rectangular with minor axis oriented parallel to the surface-normal direction, and rectangular with its major axis oriented parallel to the surface-normal direction were tested with a fixed offset height ratio of 2. A particle image velocimetry system was used to perform the velocity measurements. Various quantities were investigated, including instantaneous velocities and turbulent statistics up to the fourth order moment. The jet-surface interaction was examined using mean surface velocity, velocity defect, vorticity thickness and surface turbulence intensities. The turbulent structures in the interaction region were investigated using two-point correlations, joint probability density functions and proper orthogonal decomposition (POD). Turbulent statistics along the free surface revealed that the surface was in the state of stretching and contracting due to the alternating velocity gradient. The straining effect became more severe for shallower jet. For a given offset height ratio, the greatest mean strain at the free surface was produced by the jet issuing in the minor plane of the rectangular nozzle. This nozzle configuration also led to enhancements in the peak values of the surface velocity (about 37%) and turbulence intensities (up to 24%) compared to the circular, square and the jet discharged in the major plane of the rectangular nozzle. The two-point correlations and POD results indicated that the spatial coherence of the velocity fluctuations reduced in the upper shear layer than the lower shear layer. Shorter offset height ratio experienced a slower fractional energy convergence due to a reduction in the structure size under confinement. The re-orientation of the rectangular nozzle to major axis increased the spatial coherence in the interaction region, which led to an about 21% higher fractional energy contribution of the most dominant POD mode (the first mode) compared to the other configurations.