The shortest possible summary of MHC I can manage. This includes spoilers i.e. information that was not available at the time.
Corat, Wheel of the Wind, was hauled up by a Dominican Triad for leading pilgrims to Yasukuni, a Shinto war shrine. He got snotty with the triad and Michael interfered, so he was convicted. What was left of Corat after his sentence was rehabilitated by a team of War's special forces, The Corps. After training he was quietly hired by Nisroc, word of Spies, to recruit a group of humans who Hell would not recognize as servitors of Heaven.
Michael sent his servitors to Yves' library to check the balances of the potential recruits' Fates and Destinies. Yves noticed an awful lot of Warbirds in his library, unusual for them, and confronted Michael. Being a seraph, he told Yves what he was up to. Yves, not being a seraph, concocted a cover story for when other angels inevitably noticed something going on. That cover story was the Mile Higher Club.
Corat was to recruit a random or seemingly random group of angels who should not be able to function as a team, due to differences in personalities and service. He was to set them to a task, any task, where his recruits might be inserted, to discover whether an angel would recognize them as soldier material and whether they could get along with the recruits.
Corat heard from a Mercurian friend that there was to be an angel summoning ritual at a Goth festival near L.A., and that it would include Ryuki Watari--one of Corat's recruits, but also someone known to be pursuing the possibility that angels could be summoned. They arrived to see Gavin Russo, a sorcerer and acquaintance of Ryuki's, invoke the Baron Samedi with the help of the demon Pepito. He brings the party along to witness the chaos, including some thugs blocking the door which activates Corat's Discord and Ryuki banishing Pepito on the fly.
Pepito had been a thorn in Corat's side for a couple of years, having taken the place of a dead teenager with a doting mother. Corat couldn't kill the demon without sending the kid's mother into a spiral of grief, and his kindness meant he was flirting with his own Ofanite death spiral--inaction in the face of evil.
But it does beg the question--someone throws a ritual to summon angels, and a bunch of them show up. Corat volunteers that he and Ryuki know each other, and
sets up a meeting at a hotel suite to ask what he knows about what happened. Payment for that information: get to meet a seraph in person. Ryuki takes it, but wards the hotel suite. The ward is experimental to see if it will hold an angel, but it's also a gambit to tell the other angels that Corat has a problem (Discord) that needs attention. The meeting is tense--a working ward and a set of live katanas, and Ryuki at least as afraid of them as they are of him. He tells them what he knows of Gavin.
All Soul's Night, there's an infernally-provoked shootout at a cemetery in Watts. A large number of casualties, but one stands out. Gavin Russo walks through the gunfight like he's immortal, in front of dozens of witnesses. He takes three bullets before walking back to his apartment.
A Disturbance that large in hostile territory is a mission for The Corps, the same unit Corat trained with after Yasukuni. They stop at the Creation tether to gather information before cleaning up the demon mess. (The Creation tether is a soul food restaurant, the Watts towers tether having been broken in 2000.) They feign that Corat's in trouble and frog walk him out, expecting him to identify Gavin and Pepito who they've learned are involved in the massacre. Instead they discover Corat's Discord and get orders that he is not to have contact with Pepito at any cost. Corat declines help for the Discord, for now, knowing that investigating its cause would reveal his true mission (Pepito is a classmate of recruit Danae, the psychic schoolgirl who knows him for what he is).
They track down Gavin, who is no longer possessed and is moaning pitifully at his bullet wounds. The Baron possesses him momentarily, startling the team's Ofanite who takes off his head. They find an altar that reveals who his possessor was.
The team meets to figure out how best to remove Pepito. Pepito throws a party at his current girlfriend's house in the orange groves of Riverside, hoping to murder them all humorously to please Kobal. Pepito is unpopular though, and instead of a bunch of goths showing up his brother and their beer-keg reality show friends show up. Pepito drugs them, and the party has to save their lives. They get an unexpected assist from Pepito's supervisor Vato, who's so unimpressed with his minion shacking up with an ethereal that he throws him to the angels. The angels arrange an exorcism, so Pepito's vessel will remain and maintain the illusion of a teenager gone wrong, not a demon. This is meant to soften the blow for Pepito's mother, and goes mostly as planned. After Pepito is exorcised his remnant is pathetic and sweet, creating division within the party about whether it should be allowed to live.