By using the nonequilibrium Green’s function technique, the charge and spin transport properties through an A-B interferometer that has a parallel-coupled double-quantum-dot molecule embedded in each arm, (named as parallel-coupled double-quantum-dot molecule A-B interferometer) are investigated. In the absence of magnetic flux, as compared with the A-B interferometer with two quantum dots embedded in each arm, electron tunnelling becomes far easier for parallel-coupled double-quantum-dot molecule A-B interferometer. When the magnetic field is introduced, one can observe in the conductance spectrum one Fano resonance and one anti-resonance, both of which will die away simultaneously when the magnetic flux takes a proper value. Besides, spin transport can be manipulated by tuning the bias voltage between the two leads, magnetic flux, and Rashba spin orbit interaction.