One passage comes after Huck pulled the prank on the lifeboat where he became separated from Jim and tried to make Jim believe that he had just dreamt the entire scary episode in the fog. It was a cruel joke to play, but up until this point in the book, Huck didn't really see Jim as a person with real feelings to consider. But Jim was so upset at Huck's degrading lie that Huck felt bad, and in a significant passage at the end of chapter 15, he apologizes to Jim and states, "I warn't ever sorry for it afterward, neither." This shows that Huck is making progress, and seeing Jim as a person and not just an object or a slave.
A second and third passage comes in the next chapter when they run across a boat and Huck paddles out in the canoe determined to turn Jim in as a runaway slave. The first passage is when Huck is mad that Jim has plans to buy his wife and children back. He states,
"Here was this nigger...coming out flat-footed and saying he would steal his children--children that belonged to man...that hadn't ever done me no harm."
This passage shows how Huck still has lingering strands of the Southern attitude that slaves weren't people, and were owned by their masters. However, when he tries to turn Jim in, he can't. Instead, he concocts a lie about his dad having the smallpox on the raft, in order to keep the men away. This shows that Huck is continuing to come to the realization that Jim is more than just property to be sold and bought.
A third passage comes at the end of the book when Jim stays with the wounded Tom Sawyer while Huck goes to get a doctor. Huck writes that he knows he can trust Jim to stay, even if it meant he was giving up his freedom, because he "know'd Jim was white on the inside." This shows that Huck finally feels that Jim is his equal. They are on equal ground, as friends, and Huck respects him.
I hope that helped; good luck!