Hydraulic lower limb exoskeletons are wearable robotic systems, which can help people carry heavy loads. Recently, underactuated exoskeletons with some passive joints have been developed in large numbers for the purpose of decreasing the weight and energy consumption of the system. There are many control algorithms for a multi-joint fully actuated exoskeleton, which cannot be applied for underactuated systems due to the reduction in the number of control inputs. Besides, since the hydraulic actuator is not a desired force output source, there exist high order nonlinearities in hydraulic exoskeletons, which makes the controller design more challenging than motor driven exoskeleton systems. This paper proposed a precision interaction force controller for a 3DOF underactuated hydraulic stance leg exoskeleton. First, the control effect of the wearer is considered and the posture of the exoskeleton back is assumed as a desired trajectory under the control of the wearer. Under this assumption, the system dynamics are changed from a 3DOF underactuated system in joint space to a 2DOF fully actuated system in Cartesian space. Then, a three-level interaction force controller is designed in which the high-level controller conducts human motion intent inference, the middle level controller tracks human motion and the low-level controller achieves output force tracking of hydraulic cylinders. The MIMO adaptive robust control algorithm is applied in the controller design to effectively address the high order nonlinearities of the hydraulic system, multi-joint couplings and various model uncertainties. A gain tuning method is also provided to facilitate the controller gains selection for engineers. Comparative simulations are conducted, which demonstrate that the principal human-machine interaction force components can be minimized and good robust performance to load change and modeling errors can be achieved.