Hexahedral mesh generation using overlay grid methods has the benet of being fully automatic, requiring minimal user input. These methods follow a mesh-rst approach where an initial mesh, usually a grid, is used to overlay the reference geometry. Procedures to modify the initial mesh are then employed to best capture the geometry to get a conformal all-hex mesh [1]. One of the main drawbacks of those methods is the resulting mesh quality. While the interior of the mesh remains the same as the initial mesh, cells located at the material interfaces can end up quite deformed or even inverted, making the mesh totally useless for most numerical simulation codes. Considering an input mesh carrying volume fractions of the materials, the main purpose of the presented work is to ensure a minimal cell quality. Our method draws upon the overlay grid pipeline described in [2] where several steps (cell assignment correction, interface reconstruction, mesh adaptation) are altered to control cell quality.