The dynamics of free-surface fluid flows, possibly interacting with highly deformable structures, is a complex problem, still attracting considerable attention. The Particle Finite Element Method (PFEM) is a mesh-based Lagrangian approach well-suited for such problems as it naturally tracks fluid boundaries and the Fluid-Structure Interaction (FSI) interface through the positions of mesh nodes. However, in scenarios with non-uniform velocity boundary conditions or in areas with large topology variations, an Eulerian formulation proves to be more convenient. To exploit the benefits of both formulations, we propose an adaptive hybrid Lagrangian-Eulerian approach in which nodes on the fluid free-surfaces and on the interfaces are treated as Lagrangian, while the remaining nodes can be either Eulerian or Lagrangian. Additionally, the transition zone between the two kinematics can be detected automatically. Within the PFEM framework, to mitigate excessive mesh distortion, once the current mesh becomes excessively distorted, a new one is created through a Delaunay tessellation. However, the 3D Delaunay tessellation does not assure elements with ideal geometrical properties, introducing the possibility of nearly zero volume elements (slivers). The presence of even a single sliver impacts dramatically explicit analyses, resulting in a drastic reduction of the stable time step size. To mitigate this issue, badly shaped elements are merged to the neighbours, forming Virtual Elements of arbitrary shapes characterized by a larger stable time step size.