Open-circuit-voltage (OCV) data is widely used for characterizing battery properties under different conditions. It contains important information that can help to identify battery state-of-charge (SOC) and state-of-health (SOH). While various OCV models have been developed for battery SOC estimation, few have been designed for SOH monitoring. In this paper, we propose a unified OCV model that can be applied for both SOC estimation and SOH monitoring. Improvements in SOC estimation using the new model compared to other existing models are demonstrated. Moreover, it is shown that the proposed OCV model can be used to perform battery SOH monitoring as it effectively captures aging information based on incremental capacity analysis (ICA). Parametric analysis and model complexity reduction are also addressed. Experimental data is used to illustrate the effectiveness of the model and its simplified version in the application context of SOC estimation and SOH monitoring.