An important question in feedback control design is how to achieve desired performance for dynamical systems subject to both model uncertainties and white noise. For this purpose, it is desirable to develop a systematic design technique that combines the good aspects of both H(2)(LQG) and H(infinity) methods, which provides the motivation for the development of multiobjective design framework in this paper. Encouraged by a time domain game approach for H(2)/H(infinity) control design, two multiobjective control design problems are formulated and solved in the time domain. Results for both the finite time horizon and the infinite time horizon are presented. It is shown that all the results can be obtained by solving the corresponding set of coupled Riccati equations.