Contact mechanics is a special type of interface problem that governs numerous engineering problems, such as adhesion, wear and thermomechanical effects. Many computational techniques based on the finite element method (FEM) have been developed to address these problems. Nevertheless, some drawbacks persist. These include the non-smooth representation of curved contact surfaces and the limitation to C^0 continuity at inter-element boundaries, resulting in a discontinuous field of normal vectors. To overcome these drawbacks, approaches based on isogeometric analysis (IGA) have been developed. These approaches use NURBS-based meshes to smoothly represent the contact surfaces and can achieve arbitrary continuity at inter-element boundaries. However, the propagation of this higher-order continuity into the bulk domain does not appear advantageous, as it does not necessarily improve the spatial convergence rate due to the reduced regularity of unilateral contact problems. Therefore, we propose separating the discretization of the contact boundary and the bulk domain on each of the bodies in contact. The contact boundary is discretized using an isogeometric boundary layer mesh, thus allowing to smoothly represent the contact interface. The bulk domain is represented using a Cartesian mesh, which can be based on either isogeometric elements or classical Lagrangian finite elements. This approach shares similarities with the so-called immersed boundary-conformal method (IBCM). The resulting discretization leads to an embedded mesh problem, where the boundary layer mesh must be coupled with the underlying Cartesian mesh at the boundary layer's inner surface. We achieve this by defining a discrete Lagrange multiplier field, following the principles of classical mortar methods. Possible stability issues might arise due to the well-known violation of the inf-sup condition. It can be demonstrated, that in our case, where both boundary layer and Cartesian meshes share the same material properties, the violation of the inf-sup condition does not affect the usability of our method. This talk addresses the building blocks for discretization schemes for embedded mesh tying constraints between isogeometric boundary layer meshes and Cartesian meshes, with applications to contact problems. Moreover, different methods for generating boundary layers are presented. Finally, several quantitative and qualitative examples demonstrate the numerical properties of the proposed approach.