We present how a humanoid robot, called Acroban, allows whole-body robust, natural and intuitive physical interac- tion with both adults and children. These physical human-robot interaction are made possible through the combination of several properties of Acroban: 1) it is whole-body compliant thanks to variable impedance control and also thanks to the use of elastics and springs; 2) it has a bio-inspired vertebral column allowing more flexibility in postural and equilibrium control; 3) it is light- weight; 4) it has simple low-level controllers that leverage the first three properties. Moreover, the capabilities for physical human- robot interaction that we show are not using a model of the human, and in this sense are "model free": 1) the capability of the robot to keep its equilibrium while being manipulated or pushed by humans is a result of the intrinsic capability of the whole body to absorb unpredicted external perturbations; 2) the capability of leading Acroban by the hand is an emergent human-robot interface made possible by the self-organizing properties of the body and its low-level controllers and was observed a posteriori only after the robot was conceived and without any initial plan to make this possible. Finally, an originality of Acroban is that is is made with relatively low-cost components which lack of precision is counterbalanced with the robustness due to global geometry and compliance.