Battery aging is a natural process that contributes to capacity and power fade, resulting in a gradual performance degradation over time and usage. State-of-charge (SOC) and state-of-health (SOH) monitoring of an aging battery poses a challenging task to the battery management system (BMS) due to the lack of direct measurements. Estimation algorithms based on an electrochemical model that considers the impact of aging on physical battery parameters can provide accurate information on lithium concentration and cell capacity over a battery's usable lifespan. A temperature-dependent electrochemical model, the enhanced single particle model (ESPM), forms the basis for the synthesis of an adaptive interconnected observer that exploits the relationship between capacity and power fade, due to the growth of solid electrolyte interphase layer (SEI), to enable combined estimation of states (lithium concentration in both electrodes and cell capacity) and aging-sensitive transport parameters (anode diffusion coefficient and SEI layer ionic conductivity). The practical stability conditions for the adaptive observer are derived using Lyapunov's theory. Validation results against experimental data show a bounded capacity estimation error within 2% of its true value. Furthermore, the effectiveness of capacity estimation is tested for two cells at different stages of aging. Robustness of capacity estimates under measurement noise and sensor bias is studied.