The results of an experimental study carried out to investigate the structure of turbulence near a shear-free density interface are presented. The experimental configuration consisted of a two-layer fluid medium in which the lower layer was maintained in a turbulent state by an oscillating grid. The measurements included the root-mean-square (r.m.s.) turbulent velocities, wavenumber spectra, dissipation of turbulent kinetic energy and integral lengthscales. It was found that the introduction of a density interface to a turbulent flow can strongly distort the structure of turbulence near the interface wherein the horizontal velocity components are amplified and the vertical component is damped. The modification of r.m.s velocities is essentially limited to distances smaller than about an integral lengthscale. Inspection of spectra shows that these distortions are felt only at small wavenumbers of the order of the integral scale and a range of low-wavenumbers of the inertial subrange; the distortions become pronounced as the interface is approached. Comparison of the horizontal velocity data with the rapid distortion theory (RDT) analyses of Hunt & Graham (1978) and Hunt (1984) showed a qualitative agreement near the interface and a quantitative agreement away from the interface. On the other hand, the RDT predictions for the vertical component were in general agreement with the data. The near-interface horizontal velocity data, however, showed quantitative agreement with a model proposed by Hunt (1984) based on nonlinear vortex dynamics near the interface. The effects due to interfacial waves appear to be important for distances less than about 10% of the integral lengthscale. As a consequence of the non-zero energy flux divergence, the introduction of a density interface to oscillating grid turbulence increases the rate of dissipation in the turbulent layer except near the interface, where a sharp drop occurs. The present measurements provide useful information on the structure of turbulence in shear-free boundary layers, such as atmospheric and oceanic convective boundary layers, thus improving modelling capabilities for such flows.