The equilibrium current-phase structure of a tri-terminal superconducting Josephson junction (bijunction) is analyzed as a function of the two relevant phases. The bijunction is made of two noninteracting quantum dots, each one carrying a single level. Nonlocal processes coupling the three terminals are described in terms of quartet tunneling and pair cotunneling. These couplings are due to nonlocal Andreev and cotunneling processes through the central superconductor S 0, as well as direct interdot coupling. In some cases, two degenerate midgap Andreev states appear, symmetric with respect to the (π,π) point. The lifting of this degeneracy by interdot couplings induces a strong non-local inductance at low enough temperatures. This effect is compared to the mutual inductance of a two-loop circuit.