Despite significant development effort for contact mechanics discretization methods in the classical finite element method (FEM), some key drawbacks still persist. Some of them are the non-smooth representation of curved contact surfaces and the limitation to C^0 continuity at inter-element boundaries, thus leading to a non-continuous field of normal vectors. To overcome these drawbacks, approaches based on isogeometric analysis (IGA) have been developed. These use a NURBS-based mesh to represent complex (contact) surfaces smoothly and can achieve arbitrary continuity at the inter-element boundaries. However, the propagation of this higher-order continuity into the bulk volume of the domain might not be needed for non-smooth problem classes due to their inherently reduced regularity, such as unilateral contact. In our proposed approach, we combine the advantages of IGA and FEM, distinguishing between the discretization of the body's contact interface and its interior. The contact interface, represented by a NURBS curve or surface, is extruded towards the interior to create a NURBS boundary layer mesh. Moreover, the inner bulk volume is discretized with a Cartesian finite element grid in the reference configuration. Some of these bulk elements intersect with the inner surface of the IGA boundary layer mesh. We couple the overlapping meshes using a mortar-based embedded mesh method. While this approach delivers good results under certain assumptions, possible stability issues are expected due to the well-known violation of the inf-sup condition.