This paper proposes a new class of filtering power dividers integrated with phase shifter and impedance transformer simultaneously for the first time. In contrast to the conventional approaches, the proposed filtering power dividers consist of two asymmetrical generalized bandpass networks, that can achieve arbitrary constant phase difference and good isolation at two output ports. On the one hand, the magnitude and phase properties of two generalized nth-order bandpass networks are systematically studied and fully considered to realize the prescribed power division, filtering function, constant phase difference, and impedance transformation in the co-design. On the other hand, in order to obtain good isolation, the resonator's type and impedance of these two asymmetrical networks are carefully considered and closed-form formula of isolation resistor is also deduced. Theoretical results show that the proposed topology can achieve perfect isolation over entire passband for the arbitrary phase difference. Meanwhile, the synthesis procedures are presented for a quick design process. Finally, two porotypes (90° power divider and 120° power divider) with specified different operation bandwidth (15% and 25%), filter order (3rd and 6th), and terminated port impedances (50Ω and 100Ω) are synthesized, fabricated, and tested to verify the proposed design method and predicted frequency responses. It firstly integrates the power divider, filter, phase shifter, and impedance transformer into single component and has several additional advantages, such as low cost, simple geometry, small phase deviation and amplitude imbalance, and easiness for design and fabrication.