All-inorganic perovskite (CsPbX3, X=Br or I) solar cells demonstrate superior stability while the power conversion efficiency (PCE) lags behind the organic-inorganic hybrid counterparts mainly due to the limitation of narrow absorption bands. To broaden its absorption spectrum and improve its PCE, all-inorganic perovskite/organic integrated solar cells (ISCs) utilizing CsPbI2Br as ultraviolet visible light (UV-vis) absorber and PBDTTT-E-T:IEICO as near-infrared (NIR) absorber are demonstrated in this work. The ISCs exhibit a broadened photo-response to over 900 nm attributing to the integration of PBDTTT-E-T:IEICO. The additional absorption enhances the short-circuit current density (Jsc) from 14.78 mA/cm2 to 15.98 mA/cm2, resulting greatly improved PCE of 14.03% for ISCs, much higher than that of the control perovskite solar cells (PSCs) (12.53%) and organic solar cells (OSCs) (7.51%). In-depth understanding about the charge transfer dynamic process in CsPbI2Br/PBDTTT-E-T:IEICO film is comprehensively analyzed by photoinduced transient absorption spectroscopy (TAS). Furthermore, the air stability and thermal stability of the ISCs are greatly enhanced. For unencapsulated ISCs, the PCE still preserve 95% of its initial value after aging for 300 hours in an ambient environment and the PCE retains about 90% of its original value even after aged at 85 ℃ for 180 hours in nitrogen.