Integrated states/faults observers for two-dimensional (2-D) linear systems, which can simultaneously estimate system states and faults, are studied in this study. Multiple channel faults, occurring in both measurement equation and state equation, are considered. On the basis of the singular system observer method and stability theory, asymptotically stable observers and uniformly ultimately bounded observers are proposed for the 2-D systems. For these two cases, constructive methods for observer design and parameter tuning are further provided. Under different system conditions, the necessary and sufficient conditions for the existence of integrated observers are derived and proved through matrix rank analysis. Finally, two examples are given to demonstrate the performance of the proposed methods.