Summary: In a previous work [ibid. 55, No. 9, 867–897 (2007; Zbl 1388.76253)], we presented a two-phase level set method to simulate air/water turbulent flows using curvilinear body-fitted grids for ship hydrodynamics problems. This two-phase level set method explicitly enforces jump conditions across the interface, thus resulting in a fully coupled representation of the air/water flow. Though the method works well with multiblock curvilinear grids, severe robustness problems were found when attempting to use it with overset grids. The problem was tracked to small unphysical level set discontinuities across the overset grids with large differences in curvature. Though negligible for single-phase approaches, the problem magnifies with large density differences between the phases, causing computation failures. In this paper, we present a geometry-based level set method for curvilinear overset grids that overcomes these difficulties. The level set transport and reinitialization equations are not discretized along grid coordinates, but along the upwind streamline and level set gradient directions, respectively. The method is essentially an unstructured approach that is transparent to the differences between overset grids, but still the discretization is under the framework of a finite differences approach. As a result, significant improvements in robustness and to a less extent in accuracy are achieved for the level set function interpolation between overset grids, especially with big differences in grid curvature. Example tests are shown for the case of bow breaking waves around the surface combatant model David Taylor Model Basin (DTMB) 5415 and for the steady-state ONR Tumblehome DTMB 5613 with superstructure. In the first case, the results are compared against experimental data available and in the second against results of a semi-coupled method.