The inverted pendulum is by nature a dynamically unstable system and may be subjected to severe disturbances due to its environmental or loading conditions. This paper formulates a design for a nonlinear controller to balance a two-wheeled mobile robot (TWMR) based on Model Reference Adaptive Control. The proposed solution overcomes the limitations of control systems that rely on fixed parameter controllers. Given the nonlinear single-input multi-output (SIMO) nature of the TWMR platform, the proposed adaptive controller can handle non-linearities without the need for linearization, and inherently dealing with SIMO systems. By studying the influence that hidden dynamic effects can cause, we show the preference of the proposed controller over other designs. Simulation results demonstrate the applicability and efficiency of our proposed design, and experimental results validate the effectiveness of the proposed scheme in guaranteeing asymptotic output tracking, even in the presence of unknown disturbances.