We have fabricated and investigated three-terminal Nb/Al-AlOx-Nb/Al-AlOx-Nb tunnel devices with a thin (≈ 13 nm) Nb/Al middle layer. By measuring I-V characteristics and Ic vs. H dependences of the whole device and particular junctions separately, we have demonstrated strong interaction between the junctions. As a result, at V = 0 the system behaves like a single junction. The pronounced feature of this state is the critical current locking of the junctions, with a `common' critical current larger than the critical currents of the individual junctions. This state can be characterized by identical phase difference distributions for both junctions, and is stable at least for the region of superconducting current and magnetic field values corresponding to the first period of the diffraction pattern of the whole structure. At V = 0 and some value of magnetic field near to that where critical current of the system first falls to zero, the system undergoes a transition into the 2D state, in which the individual junctions have different phase distributions and behave relatively independently. In a high magnetic field, when many vortices enter the multilayer structure, along with the current locking, there is evidence of phase locking.