Accurate estimations of battery energy and available power capability are of great of importance for realizing an efficient and reliable operation of electric vehicles. To improve the estimation accuracy and reliability for battery state of energy and power capability, a novel model-based joint estimation approach has been proposed against uncertain external operating conditions and internal degradation status of battery cells. Firstly, it proposes a three-dimensional response surface open circuit voltage model to calibrate the estimation inaccuracies of battery state of energy. Secondly, the adaptive unscented Kalman filter (AUKF) is employed to develop a novel model-based joint state estimator for battery state of energy and power capability. The AUKF algorithm utilizes the well-known features of the Kalman filter but employs the method of unscented transform (UT) and adaptive error covariance matching technology to improve the state estimation accuracy. Thirdly, the proposed joint estimator has been verified by a LiFePO4 lithium-ion battery cell under different operating temperatures and aging levels. The result indicates that the estimation errors of battery voltage and state-of-energy are less than 2% even if given a large erroneous initial value, which makes the state of available power capability predict more accurate and reliable for the electric vehicles application.