A quick update on Mustafic: In the recent judgement of Al-Jedda, it seems that the Grand Chamber of the European Court of Human Rights at least considered the possiblity that the UN and the coalition might have both been the "principal" of the coalition forces in Iraq:
80. The Court does not consider that, as a result of the authorisation contained in Resolution 1511, the acts of soldiers within the Multi-National Force became attributable to the United Nations or – more importantly, for the purposes of this case – ceased to be attributable to the troop-contributing nations. The Multi-National Force had been present in Iraq since the invasion and had been recognised already in Resolution 1483, which welcomed the willingness of Member States to contribute personnel. The unified command structure over the force, established from the start of the invasion by the United States and United Kingdom, was not changed as a result of Resolution 1511. Moreover, the United States and the United Kingdom, through the Coalition Provisional Authority which they had established at the start of the occupation, continued to exercise the powers of government in Iraq. Although the United States was requested to report periodically to the Security Council about the activities of the Multi National Force, the United Nations did not, thereby, assume any degree of control over either the force or any other of the executive functions of the Coalition Provisional Authority.
Cf. Marko Milanovic's writeup of this case and the related case of Al-Skeini on EJIL:Talk!