This paper studies a two-degree-of-freedom (2DOF) design method of robust servo systems for step references and disturbances in the setting of output feedback. Specifically, we consider the introduction of a state observer and show that the fundamental desirable properties (i.e. 2DOF nature) attained in the state feedback case are inherited, qualitatively speaking, to the output feedback case. At the same time, we quantitatively clarify the performance deterioration about disturbance rejection caused by the introduction of an observer.