Just after escaping the North Pole in the movie, the Centipede takes his task of navigating the peach very seriously, to the point where he tries to fend off sleep in order to do so. And just as he desperately tries to force himself not to doze off, the Grasshopper (who had earlier knocked out one of Centipede's teeth in anger), comes to relieve him of his post. By bringing him a chair and blanket, and playing him off to sleep with his violin. D'awwww...
Centipede: (sleepily) Thanks Mr. Grasshopper...
When Miss Spider is making James's bed, he asks her why she's so kind to him. She replies because he was kind to her first, since she was the spider he rescued from his aunts earlier in the movie.
Although they've been rather viciously snarking at each other up til then, after the Centipede dives into the water, Miss Spider is very quick to volunteer to help James save him—and when their first attempt fails, immediately heads down to try again. Not to mention the kiss on the cheek she gives him when it turns out he's all right.
A blink and you'll miss it entry—during the song That's the Life For Me, Mrs. Ladybug throws Mr. Grasshopper his top hat and cane. They have obviously already been good friends for some little while, if they are comfortable with Mrs. Ladybug toting around his spare accoutrement in such a way. They seem to be very in tune with each other, since she throws them to him precisely when he needs them.
At the very end, James and the insects all live together in a house made out of the peach's pit — as a family.
When James literally drops in on the group, the bugs could've easily reacted badly to a human in their midst. Instead, they comfort, befriend, and later adopt James as their own because they don't see him as just a human, but as frightened child who's just as vulnerable as they once were.
Another blink and you'll miss it entry. When James first falls asleep, his coat is merely draped over him, courtesy of Miss Spider. When he makes up, the coat is wrapped around him like a blanket. Some one had obviously checked on him and wrapped the coat more tightly around him.