The two-phase turbulent flow past an interface-piercing circular cylinder is studied using a high-fidelity orthogonal curvilinear grid solver with a Lagrangian dynamic subgrid-scale model for large-eddy simulation and a coupled level set and volume of fluid method for air-water interface tracking. The simulations cover the sub-critical and critical and post critical regimes of the Reynolds and sub and super-critical Froude numbers in order to investigate the effect of both dimensionless parameters on the flow. Significant changes in flow features near the air-water interface were observed as the Reynolds number was increased from the sub-critical to the critical regime. The interface makes the separation point near the interface much delayed for all Reynolds numbers. The separation region at intermediate depths is remarkably reduced for the critical Reynolds number regime. The deep flow resembles the single-phase turbulent flow past a circular cylinder, but includes the effect of the free-surface and the limited span length for sub-critical Reynolds numbers. At different Froude numbers, the air-water interface exhibits significantly changed structures, including breaking bow waves with splashes and bubbles at high Froude numbers. Instantaneous and mean flow features such as interface structures, vortex shedding, Reynolds stresses, and vorticity transport are also analyzed. The results are compared with reference experimental data available in the literature. The deep flow is also compared with the single-phase turbulent flow past a circular cylinder in the similar ranges of Reynolds numbers. Discussion is provided concerning the limitations of the current simulations and available experimental data along with future research.