Superconducting radio frequency (SRF) cavities, which are critical components in many particle accelerators, need to be operated in the Meissner state to avoid strong dissipation from magnetic vortices. For a defect-free superconductor, the maximum attainable magnetic field for operation is set by the superheating field, B_sh, which directly depends on the surface current. In heterostructures composed of different superconductors, the current in each layer depends not only on the properties of the individual material, but also on the electromagnetic response of the adjacent layers through boundary conditions at the interfaces. Three prototypical bilayers [Nb_1−xTi_xN (50 nm)/Nb, Nb_1−xTi_xN (80 nm)/Nb, and, Nb_1−xTi_xN (160 nm)/Nb] are investigated here by depth-resolved measurements of their Meissner screening profiles using low energy muon spin rotation (LE-µSR). From fits to a model based on London theory (with appropriate boundary and continuity conditions), a magnetic penetration depth for the thin Nb_1−xTi_xN layers of λ_Nb1−xTixN = 182.5(31) nm is found, in good agreement with literature values for the bulk alloy. Using the measured λ_Nb1−xTixN, the maximum vortex-free field, Bmax, of the superconductor-superconductor (SS) bilayer structure was estimated to be 610(40) mT. The strong suppression of the surface current in the Nb_1−xTi_xN layer suggests an optimal thickness of ∼ 1.4 λ_Nb1−xTixN = 261(14) nm.