In this article, we propose a control method, providing mobile robots with whole-body compliance capabilities, in response to multi-contact physical interactions with their environment. The external forces applied to the robot, as well as their localization on its kinematic tree, are measured using a multimodal, self-configuring and self-calibrating artificial skin. We formulate a compliance control law in Cartesian space, as a set of quadratic optimization problems, solved in parallel for each limb involved in the interaction process. This specific formulation makes it possible to determine the torque commands required to generate the desired reactive behaviors, while taking the robot kinematic and dynamic constraints into account. When a given limb fails to produce the desired compliant behavior, the generalized force residual at the considered contact points is propagated to a parent limb in order to be adequately compensated. Hence, the robot's compliance range can be extended in a both robust and easily adjustable manner. The experiments performed on a dual-arm velocity-controlled mobile manipulator, show that our methodology is robust to nullspace interactions and robot physical constraints.