This is a surprisingly effective -- as well as gutsy -- crossover, and somehow manages to get away with fewer contortions than almost any other intercompany crossover yet.
The Punisher has agreed to help the government capture a small-time thug nicknamed Red so the government can interrogate him and otherwise use him to bring down a number of big-time killers. Because the government needs Red in good health, and because Red's interrogations and testimony will virtually guarantee the ruin of a number of major killers, the Punisher has agreed this one time to avoid killing or even seriously injuring Red. He tracks Red to an out-of-the-way small city called Riverdale. In true Marvel Comics fashion, The Punisher finds the sight of such happy, safe families triggers a few panels of remembered sorrow over his own personal tragedies. In true Archie Comics fashion, Red turns out to be nearly identical in appearance to Archie Andrews and manages to impersonate him.
What makes this crossover work is that both comic realities remain true to themselves to a degree most Marvel/DC crossovers never achieve. The agreement Punisher has with the government enables the storyline to establish a rare liminal area where both comic realities can briefly overlap. The Punisher realizes that the people of Riverdale are blesed to live the life he would love to have lived with his wife and child, so he vows to go out of his way to protect the Riverdale world from any exposure to the violence of his own world. His refusal to bring Punisher-style violence into Archie's high school world comes across as a deliberate (and occasionally rather difficult) effort on the part of the Punisher that fits believably into his established history and character of the time, rather than a belaboredl conceit for the sake of the crossover. Similarly, the various Riverdale characters respond to the Punisher as this exotic and mysterious figure of legender they have read about in newspapers, from the exotic and mysterious big city of legend called New York which, of course, none of them (except the Lodges) has ever visited.
The Archie characters enjoy their usual whimsical humor in the sequences without the Punisher present but show their more adventure-tale side during the scenes shared with the Punisher. For example, Veronica Lodge is kidnapped at one point by Red in a fashion that implies possible sexual violence to a hardcore Marvel reader while implying only an unspecified threat to a reader who is familiar only with Archie comic books. Veronica is able to fight back believably as one of the few Archie characters who has ever been shown to know self-defense techniques (due to her background as the daughter of one of the world's wealthier families).
It is difficult to imagine any way to write a believable sequel to this crossover, but the writers deserve far more credit than they are usually given for somehow pulling it off this one time.