Aufidius is a big, bad Volscian general, which automatically makes him Coriolanus' arch enemy. But Tullus Aufidius isn't exactly the Joker to Coriolanus' Batman. Although there's an intense, long-standing rivalry between these two guys, they totally respect each other as soldiers. In fact, they're always giving each other compliments and hugs, even though they still totally want to kill each other. (Hey, relationships are confusing.)
When Coriolanus finds out Rome is going to war with the Volsces, he says "They have a leader, / Tullus Aufidius [...] I sin in envying his nobility"(1.1.228-230). Coriolanus also says that Aufidius "is a lion" that he is "proud to hunt"(1.1.235-236). Compare the "lion" compliment to little animal nicknames Coriolanus has for the plebeians, like "curs" [dogs], "hares" [kind of like rabbits], and "geese" (1.1.168-172). (More on this in "Symbols: Animal Imagery.")
In other words, Coriolanus considers Aufidius to be a noble adversary. He has more respect for an enemy soldier than he has for his own people—which tells us something about how important military heroism is in this play.
In fact, Aufidius and Coriolanus are so obsessed with each other that the relationship often seems a little steamy. When Aufidius finds out that Coriolanus has left Rome and wants to join the Volscians, Aufidius admits that Coriolanus gets him all hot and bothered.
Know thou first,
I loved the maid I married; never man
Sigh'd truer breath; but that I see thee here,
Thou noble thing! more dances my rapt heart
Than when I first my wedded mistress saw
Bestride my threshold. (4.5.113-118)
Yep. Aufidius just compared seeing Coriolanus to seeing his new bride in the ancient Roman version of the honeymoon suite. After comparing Coriolanus to his bride, he goes into detail about the dreams he's had about encountering Coriolanus on the battlefield:
I have nightly since
Dreamt of encounters 'twixt thyself and me;
We have been down together in my sleep,
Unbuckling helms, fisting each other's throat,
And waked half dead with nothing. (4.5.122-126)
Gee. All this talk about the two men being "down together" and "unbuckling" and "fisting" various stuff is making us want to bump up the "Steaminess" rating. What's going on?
Well, a lot of the characters in this play get all hot and bothered when they think about warfare. (Cominius says pretty much the same thing about being hot for both his wife and Coriolanus in Act 1, scene 6.) Plus, ancient Rome is a warrior culture that places a lot of emphasis on the bonds that men forge on the battlefield. When it comes down to it, this kind of talk is par for the course: it emphasizes that Coriolanus (and Aufidius) just can't code switch so easily. They can't go from being manly warrior men to political family men—it just doesn't work that way.
In any case, the love-fest doesn't last very long. In the end, Aufidius is so jealous of Coriolanus' popularity that he decides to get rid of him. When Coriolanus agrees to a peace treaty with Rome, Aufidius accuses Coriolanus of treason (5.6). Then he kills him. One of the final images of the play is of Aufidius standing on top of Coriolanus' corpse in triumph over our fallen hero.
Gee. Couldn't he just have defriended him?