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In this paper we investigate the action of ambient turbulence on thermohaline interleaving using both theory and numerical calculations in combination with observations from Meddy Sharon and the Faroe Front. We improve upon the highly simplified models of ambient turbulence used previously by allowing turbulent diffusivities of momentum, heat and salt to depend on background gradients and to evolve as the instability grows. Previous studies have shown that ambient turbulence, at typical ocean levels, can quench the thermohaline interleaving instability on baroclinic fronts. These findings conflict with the observation that interleaving is common in baroclinic frontal zones despite ambient turbulence. Another challenge to the existing theory comes from numerical experiments showing that the Schmidt number for sheared salt fingers is much smaller than previously assumed. Use of the revised value in an interleaving calculation results in interleaving layers both weaker and thinner than those observed. We show that, when turbulence has Prandtl number greater than unity, turbulent momentum fluxes can compensate for the reduced Schmidt number of salt fingering. Thus, ambient turbulence determines the vertical scale of interleaving. In typical oceanic interleaving structures, the observed property gradients are insufficient to predict interleaving growth at an observable level, even when improved turbulence models are used. The deficiency is small, though: gradients sharper by a few tens of percent are sufficient to support instability. We suggest that this is due to the efficiency of interleaving in erasing those property gradients. We identify a new class of mechanisms for interleaving driven by flow-dependent fluctuations in turbulent diffusivities. The underlying mechanism is similar to the well-known Phillips layering instability, but due to Coriolis effects it has a well-defined vertical scale and also a tilt angle opposite to that of finger-driven interleaving.