The analysis of free surfaces is important to better understand different chemical and physical effects. Free surfaces exist at the interface between two materials (phases) with different densities. Due to that the surface can move almost freely directed by the phase with the higher density. For reconstruction and tracking of these surfaces different approaches exist. One of these is the Volume-Of-Fluid method in which the domain is separated into cells containing a fractional value. Based on these values algorithms can track volume changes over time by reconstructing a geometrical representation of the surface and deriving shifts of volume fractions between cells. Often a surface reconstruction based on the volume fractions is therefore necessary to approximate the evolution of the surface using geometrical properties. Only few of the available methods focus on an accurate visualization. This work introduces a new approach for reconstructing and visualizing interfaces between two phases (e.g. fluid and gas) in 3D on rectilinear grids. The goal is to create a precise mesh representation by combining the Marching Cubes algorithm with the Volume-Of-Fluid approach. First, basic operations that are needed to approximate the fractional values inside the cells and reduce the overall mean curvature of the mesh are defined. After that different schemes to combine these operations as well as necessary extensions are discussed and tested in order to achieve the most accurate result possible. This results in an extended Laplacian method used for mesh smoothing. Cell volume correction is done using a Newton approach which shifts vertices along gradients scaled by volume differences. Conditional refinement of mesh triangles is added to improve the overall result. It is shown that for simple cases the approach works as intended. Yet, the overall runtime and existing boundary cases necessitates further adaptations so that it can be used on a regular basis in different scientific scenarios.