Arbiter comforts Chief after he has his feelings hurt by a stuck-up gamer he befriended named Craig, who claims to be MLG. Keep in mind, Master Chief is a HUGE Jerk ass himself who takes pride in making life miserable to everyone he meets, and for Arbiter to come to his aid tells viewers a lot about Arbiter.
The ending of Season 6.
Additionally in the same episode, when Chief goes too far with his cracks to the point where Arbtier starts crying about how awful his existence is, for Chief to try and comfort the one person he can't stand (as much as Arbiter would likewise,) shows that Chief is capable of showing compassion as well.
From "Take a Seat", some of the conversations between Chief and Hallucination!Cortana.
Hallucination!Cortana: "Maybe, somewhere deep within your mind, you're a lot smarter and have a much clearer understanding of right from wrong than you think."
From "Greenlit", Arbiter and Chief are having a conversation in the kitchen regarding Eugene's treatment of Brody and Kyle, with each of them coming to the conclusion that they shouldn't be friends with Eugene or the others anymore; Chief is disheartened by this, as he just wants a friend.
Chief: I don't care who it is, or what they've done. I just wanted one, you know? Just one.
Arbiter: I know. And you've got one.
In "Game Over", Chief and Arbiter set aside their differences to spend what little time they have left being friends.
Claire letting Arbiter know how he has made an impact on her life in "Ignition". Also, Chief telling Arbiter how he always thought of Arbiter as being really cool, and then asking for Arbiter to wait for him outside the entrance to the afterlife, so they can go in together.
The fact that season 8 is being made right now. The show going on at all gives hope that the massive depression brought on by the last episode will get brighter.