The Euler potentials for two current layers aligned to an ambient homogeneous magnetic field are found. Previous treatment of such a system assumed constant current density in the layers. However, the magnetic field becomes infinite at the edges. The new approach eliminates this inconsistency by introducing an inhomogeneous current density. Euler potentials are constructed semi-analytically for such a system. Charged-particle motion and trapping in it are examined by this representation. Using Euler potentials, the influence of current sheets of zero and non-zero thicknesses on energetic-particle fluxes is investigated, and characteristic flux variations near the sheets are presented. The results can be applied to Birkeland currents.