There are so many events to choose from here, and I would argue that in each one, Christ presents Himself as being both divine and human—because that was the entire point of His birth and ultimate sacrifice.
In John 4, Jesus meets the Samaritan woman at the well. On one hand, he presents himself as entirely human. He is thirsty as it is around noon, and the heat during this time of day would be sweltering. Most people would have retired to a shady spot for rest, yet Jesus sends his disciples away just before this woman approaches. This is where the divinity of Christ is apparent. He knew that she was on her way, and he planned this conversation. As they talked, he told her that he knew of her five previous marriages and of her current boyfriend—to whom she wasn't married at all. This lifestyle would have been an utter disgrace in this setting, and this is undoubtedly why the woman waited until most people had retired to other places before she came for water. Without ever meeting her, Jesus knew her. She was filled with an incredulous wonder; when she returned to town, she told everyone she encountered that Jesus "told [her] everything [she] ever did." In this exchange, we see that Jesus understands this woman's human needs and never admonishes her for her sinful ways. He doesn't chastise her; instead, he offers her hope. And that is the example that He expects humanity to follow.
Another example occurs in Matthew 4. In this chapter, Jesus fasted for forty days and forty nights, and Satan tempted him, saying that if he was the Son of God, He should just turn rocks into bread. Jesus responded by quoting a verse from Deuteronomy. Later, Satan offered to give Jesus all the kingdoms of the world if He would bow and worship Satan instead of God. Jesus again quoted Deuteronomy. In His humanity, we see that Jesus was physically weak. Satan was aware of this, and that is why he believed that his temptations may prove fruitful. Yet in a moment of divinity, Jesus was attended by angels when he rejected Satan for the final time. This shows Christians the power of the Holy Spirit to guide through the temptations in life. Because Jesus successfully rejected Satan in His humanity, the ability to follow this example seems more feasible than trying to follow a solely divine being who is removed from human experience and shortcomings.