As surprising as it might sound, Victor Emmanuel III was still - at least technically - Mussolini's boss... despite being called the Duce and enjoying a large degree of autonomy, he was still Italy's Prime Minister whether he liked or not (he didn't) and as such subject to the King's authority like every other good citizen. Indeed, Mussolini ended up being sacked by V.E. III on 25 July 1943 - but the King couldn't have acted without the consent of the other members of the Great Council of Fascism.
In reality, Mussolini had some kind of leverage to threaten the King with... namely, the very fact that he was the one running the country in his name and had - among the other things - an entire party, the Council and the militia (MVSN) behind him. However, his influence was balanced by the fact that both the Army and the Navy were never that much loyal to him than they were to the King (who could still emanate Royal Decrees, attempt to sack his PM and veto new laws). In short theirs was an uneasy, almost symbiotic relationship and their powers were in precarious balance; an eventual power strife may very well have resulted in civil war.