This paper investigates the problem of simultaneous road profile estimation and anomaly detection. A front half-car model is used to capture the dynamics of vehicle-road interaction where road excitations at the two wheels are treated as inputs. A multi-input observer is exploited to estimate the inputs to obtain road profile. To implement the input observer, a jump diffusion process estimator is developed to estimate the states and shown to have better performance than the Kalman filter when jumps such as potholes and bumps are present. Furthermore, a real-time road anomaly detection algorithm is designed to detect and label road anomalies such as potholes, speed bumps or road joints. The algorithms are implemented in real time on a test vehicle and experimental results are analyzed with promising performance.