The coherence of three-dimensional turbulence in the compressible mixing layer of an axisymmetric, Mach 2.49, separated flow field is investigated experimentally by means of non-time-correlated tomographic particle image velocimetry (tomo-PIV) measurements. Validation of the tomo-PIV data is performed by comparison with reliable data of the same flow field acquired using stereoscopic PIV and laser Doppler velocimetry. Statistical evidence of both hairpin vortex structures as well as counter-hairpins within the mixing layer was found by conditionally averaging the flow field measurements utilizing linear stochastic estimation. The dependence of the streamwise and transverse spatial location within the mixing layer, as well as the effect of flow field recompression on these structures is presented. The size, coherence, and angular orientation of the conventional-hairpins are shown to be strongly dependent on both the streamwise coordinate, as well as the onset of the adverse pressure gradient induced by recompression. For the counter-hairpins, however, only a mild dependence of the streamwise coordinate or the onset of recompression was found until the flow field approached the point at which low momentum fluid is turned to be recirculated upstream. These structures were found to commonly exist throughout the mixing layer and occur statistically in conjunction with one another throughout a significant transverse extent of the mixing layer. Distinct regions within the mixing layer that are statistically dominated by either conventional or counter-hairpins are identified and their implications discussed. Additionally, the dynamics of the counter-hairpin structures suggest a mechanism of potentially effective flow control which, if feasible, could have a profound impact on the net vehicle drag of a blunt-faced cylindrical body in supersonic flight.