If you want to model the cohesive layer using a mesh that is finer than the adjacent bulk material mesh, the cohesive layer should be generated as a separate mesh and tied to the bulk material using tie constraints (see Defining tie constraints, Section 15.14.1). You should create a shell geometric model to represent the surface on one side of the cohesive layer and mesh that model with the desired mesh density. You can use this mesh to create an orphan mesh from which you can generate the offset mesh. For more information, see Modeling with cohesive elements, Section 26.5.3 of the ABAQUS Analysis User's Manual.
You should use care when tying zero-thickness cohesive layers to the surrounding bulk material mesh. Use the following procedure to avoid problems:
Use the solid offset mesh tool to create the layer of cohesive elements along with the top and bottom surfaces. ABAQUS/CAE appends TopSurf and BottomSurf to the surface name prefix when it creates the two surfaces on either side of the layer of cohesive elements.
Use the stack orientation query tool to distinguish the top (brown) and bottom (purple) faces of the cohesive elements.
Tie the surfaces of the surrounding bulk material mesh to the appropriate top and bottom cohesive surfaces. When you are prompted to select a surface from the cohesive surface, click Surfaces from the right side of the prompt line and select the appropriate surface. For example, select surface name-BottomSurf to tie the bottom (purple) face of the cohesive layer to the adjacent surface of the bulk material mesh.