We perform direct numerical simulations of two immiscible and incompressible fluids in a Taylor–Couette setup by means of the finite difference and the volume-of-fluid methods (see Figure 1 for a visualisation of the typical surface structure). Taylor number Ta is fixed to 10^8, while the volume fraction of the secondary phase and the surface deformability (Weber number) are varied to investigate 1. how the interface modulates the background turbulence, and 2. how the flow fields affect the surface morphologies. Due to the presence of the secondary phase, the normalised torque is always increased compared to the single-phase flow, which is related to the additional energy required to stretch the surface. We find that the secondary phase prefers to remain in the cores of the Taylor rolls, and this character is obvious for lower volume fraction and Weber cases. Also, due to this concentration in the bulk region, the secondary phase plays little role in the convection of momentum, which describes the clear effect of the Taylor rolls on the dynamics. When focusing on the independent surface structures, the averaged droplet size as a function of the Weber number reasonably follows the Kolmogorov-Hinze scaling. However, because of the large-scale circulation and the resulting wind, we observe that the droplets are more elongated and have more break-up near the walls. This results in the different surface morphologies in the boundary layers and in the bulk, whose spatial dependence is quantified by the local surface curvatures.