State-of-charge (SOC) and capacity estimation plays an essential role in many battery-powered applications, such as electric vehicle (EV) and hybrid electric vehicle (HEV). However, commonly used joint/dual extended Kalman filter (EKF) suffers from the lack of accuracy in the capacity estimation since (i) the cell voltage is the only measurable data for the SOC and capacity estimation and updates and (ii) the capacity is very weakly linked to the cell voltage. The lack of accuracy in the capacity estimation may further reduce the accuracy in the SOC estimation due to the strong dependency of the SOC on the capacity. Furthermore, although the capacity is a slowly time-varying quantity that indicates cell state-of-health (SOH), the capacity estimation is generally performed on the same time-scale as the quickly time-varying SOC, resulting in high computational complexity. To resolve these difficulties, this paper proposes a multiscale framework with EKF for SOC and capacity estimation. The proposed framework comprises two ideas: (i) a multiscale framework to estimate SOC and capacity that exhibit time-scale separation and (ii) a state projection scheme for accurate and stable capacity estimation. Simulation results with synthetic data based on a valid cell dynamic model suggest that the proposed framework, as a hybrid of coulomb counting and adaptive filtering techniques, achieves higher accuracy and efficiency than joint/dual EKF. Results of the cycle test on Lithium-ion prismatic cells further verify the effectiveness of our framework.