This paper presents a hybrid moment of fluid-level set (HyMOFLS) method of liquid/gas interface reconstruction for the application to simulate primary atomization of liquid fuel. This method combines the moment of fluid (MOF) method and the level set framework in the coupled level set volume of fluid (CLSVOF) method. In this hybrid framework, the MOF and CLSVOF methods are used to reconstruct the interface in the under-resolved and the resolved regions of the flow, respectively. An interface surface resolution metric, computed using local interface curvature and mesh spacing, called interface resolution quality (IRQ) is introduced to identify and classify these two flow regions in the computational domain. Such a strategy classifies/tags each computational cell with MOF or CLSVOF method based on a threshold value for the IRQ in each cell. The MOF method uses liquid volume fraction as well as centroids of liquid and gas phases for liquid/gas interface reconstruction in a computational cell. The CLSVOF method uses the level set for describing the interface and liquid volume fraction for mass conservation. The phase centroids in the HyMOFLS method are computed and transported on-the-fly during the cell tagging process. The transport of the liquid volume fraction, level set, and the phase centroids are performed using a directionally split algorithm. This algorithm is coupled with the Navier-Stokes equations solver that uses ghost fluid method and consistent mass and momentum flux computation for the momentum equation. Various numerical tests that exhaustively assess the capabilities, accuracy, and computational time consumption of the HyMOFLS method under multiple flow conditions and configurations. The results from these tests suggests that the hybrid framework is capable of capturing the liquid/gas interface belonging to thin and under-resolved structures that are often encountered in simulations of turbulent atomization of liquids. Following these tests, a detailed parametric study on the threshold value of IRQ is presented to test its effect on the interface reconstruction accuracy. Finally, this hybrid framework is employed to simulate turbulent jet injection and pre-filming planar Airblast atomziation cases of engineering applications. For these complex and turbulent primary atomization cases the HyMOFLS method is found to tag the MOF and CLSVOF methods to regions of the flow appropriately. The proposed HyMOFLS method is found to achieve a balance between the accuracy and the computational cost of reconstructing the liquid/gas interface for various interface and flow configurations.