In the present study, we use particle image velocimetry (PIV) to obtain planar, two-component velocity fields in two-dimensional, turbulent mixing layers at convective Mach numbers Mc of 0.25, 0.63, and 0.76. The experiments are performed in a large-scale blowdown wind tunnel, with high-speed free-stream Mach numbers up to 2.25 and shear-layer Reynolds numbers up to 106. Specific issues relating to the application of PIV to supersonic flows are addressed. The instantaneous data are analysed to produce maps of derived quantities such as vorticity, and ensemble averaged to provide turbulence statistics. The results show that compressibility introduces marked changes in the disposition of instantaneous velocity gradients within the layer, and hence in the vorticity field. In particular, peak transverse vorticity values are seen to be confined to thin streamwise sheets under compressible conditions, with little transverse communication. The location of these sheets near the lab-frame sonic velocity suggests a sensitivity of the compressible layer to stationary disturbances. Turbulence statistics derived from the planar velocity measurements confirm previous observations of strong suppression of transverse velocity fluctuations and primary Reynolds stress as Mc increases between 0.25 and 0.76.