Final answer:
The key areas of conflict between Henry II and the Archbishop of Canterbury were centered around religious authority and the balance of power between the church and the state, with key disputes over legal jurisdiction and the church's role in governance.
Step-by-step explanation:
The two main areas of conflict between Henry II and the Archbishop of Canterbury during the Middle Ages were religious authority and church-state power. This conflict is most famously exemplified in the disagreements that Henry II had with Thomas Becket, the Archbishop of Canterbury. Henry's efforts to centralize his control and extend royal justice came into direct conflict with the church's prerogatives and led to a broader question of whether the monarch or the church held ultimate authority in certain legal and administrative matters. These tensions came to a head in different forms during the reigns of different monarchs, including Henry II's struggle with Becket, and later, Henry VIII's break with the Catholic Church which was rooted in his desire to annul his marriage to Catherine of Aragon.