Recall our 3 trinities within: nature (will + intellect + power), virtue (duty + moral ideal + personality), and narrow happiness (plan + execution + pleasure).
Jesus indeed had 2 natures that were entirely separate and unmixed with each other. He was fully God and fully man.
He also has 2 personalities, one divine, the other human, but those two were so inextricably and fully intertwined as to form a single person. For example, Jesus enjoyed not only the vision of God even while incarnated but even His full comprehension. At the same time, He had a human body including the brain. His body may have been exceeding healthy and handsome, but it was the body of a particular human being, and supplied Jesus with a unique and distinct human personality. These two personalities were united such that “who or what sort of person Jesus was” was different before and after the Incarnation.
For example, Jesus’ life on earth was enriched at least with the natural functions of the body, the deliverances of the senses, and the operation of the concupiscible and irascible appetites. And there was surely more, e.g., “Then he said to them, ‘My soul is overwhelmed with sorrow to the point of death. Stay here and keep watch with me.’ Going a little farther, he fell with his face to the ground and prayed, ‘My Father, if it is possible, may this cup be taken from me. Yet not as I will, but as you will.'” (Mt 26:38-39) As a human being, Jesus wanted to avoid the horror ahead; as God, He was perfectly resolute in His purpose. There was conflict even in His will which is the intellectual appetite, a choice to be made between the human inclination and the divine duty.
Thus, we say, as per the orthodox teaching, that Jesus was two natures and one person.
Finally, Jesus’ pursuit of happiness was a single thing. There were no separate either in reality (as for nature) or in the understanding (as for virtue) for Jesus divine and human planning and executing of His plans to achieve His goals. There were no “divine actions” and “human actions” for Jesus; there was just a single set of “Jesus’ actions” and Jesus’ enjoyments. The choices Jesus made and deeds He performed in life were all for the sake of Jesus’ good, in whatever variety of things (including humanity’s good) it consisted.
We have then that Jesus was: 2 fully separate natures, 1 personality fully interwoven or fused from 2 persons, 1 pursuit of happiness.