A coupled Conservative Level Set – Moving Mesh – Immersed Boundary method is formulated and validated against the three-dimensional gravity-driven falling drop problem. First, by employing Conservative Level-Set (CLS) method, the multiphase domain can be successfully handled, while the mass conservation is controlled. Then, by using an Arbitrary Lagrangian-Eulerian formulation (i.e. a moving mesh), the simulation domain can be optimized by reducing the domain size and by allowing an improved mesh, resulting in a computational resources saving. Finally, the use of an Immersed Boundary (IB) method allows to deal with intricate geometries. All these functionalities result in a versatile and robustness method to simulate bubbles/drops problems in complex geometries. The mentioned method was successfully used to thoroughly study the falling of a drop against a plane surface, providing detailed results including velocity evolution, mesh independence study, evolution of the vertical position of the drop, streamlines and vorticity fields, and profiles evolution.