Taylor Schilling, front, plays a fresh-faced Brooklynite sentenced to 15 months in a women’s prison in Netflix’s streaming dramedy “Orange Is the New Black.” (Barbara Nitke/NETFLIX)

Two summers ago, I took the train from Washington to Staunton, Va., to go to a wedding. The woman sitting next to me was from Maine, and she was on her way to report for a relatively short prison sentence (her crime was embezzlement, I seem to recall), at the same federal prison in West Virginia “where Martha Stewart went,” she bragged, the way freshmen talk about their college choices. Once in a while, I wonder how it all worked out for her.

If you know anything about the American penal system, then you know it was probably not the calm retreat she had hoped for. As made perfectly clear in Jenji Kohan’s magnificent and thoroughly engrossing new series, “Orange Is the New Black” (available for streaming on Netflix), prison is still the pits. But it is also filled with the entire range of human emotion and stories, all of which are brought vividly to life in a world where a stick of gum could ignite either a romance or a death threat.

Based on Piper Kerman’s memoir of the same name, the series follows a fresh-faced woman from Brooklyn (she’s launching a line of artisanal lotion!) who is arrested for her connection to an international drug operation. What happened, your honor, was this: A decade ago, Piper was in a lesbian relationship and shuttled a large sum of money to Europe for her girlfriend, who worked for a cartel. Someone has named her in an indictment, and before she knows it, Piper is sentenced to 15 months in prison.

“Orange Is the New Black” feels like Netflix’s first real home run since it famously entered the scripted-series biz. I realize some people couldn’t get enough of the contorted “House of Cards” this year, and that the “Arrested Development” niche is still dizzy from their group binge in May, but “Orange” is the first series in which I’d almost insist that viewers upgrade to streaming service and come along for television’s seemingly inevitable future delivery method.

Kohan also created Showtime’s sprawling drug-and-fractured- family saga, “Weeds,” and “Orange Is the New Black” has some of that same comi-tragic feel to it, with a whole lot more depth. Once Piper (Taylor Schilling, doing a perfectly naive little bird) is behind bars, we are introduced to a harsh yet complex array of female characters.

Having bid her boyfriend Larry (Jason Biggs) a tearful goodbye (“Promise you’re not watching ‘Mad Men’ without me,” she begs him, later), Piper quickly wises up and learns to navigate the distrustful exchanges that form her new life. She’s completely thrown to discover that one of the inmates in her wing is the ex-girlfriend (“That ’70s Show’s” Laura Prepon) who got her in all this trouble to begin with.

Watching the show, one begins to realize that all the good parts for women truly have been kept locked up somewhere; now, here they all are, free (in at least one sense) to be portrayed. Within the first six episodes, they are expertly and fully sketched, textured and realized: Latinas, lesbians, an activist nun, a fireman who transitioned into a woman, a housekeeper-turned-murderer, a Russian inmate (Kate Mulgrew) who runs the kitchen and serves Piper a used-tampon sandwich out of initial spite. (Warning: The show is full of gross and intentionally unsettling moments; it is a prison, after all. With any luck, the sandwich will be the worst of it.)

Together, these women and their stories form a sad and strange tapestry, but “Orange Is the New Black” is by no means a female “Oz.” And although there are unwanted advances from unctuous guards (including Pablo Schreiber as Officer Mendez, a.k.a. “Pornstache”), it has little use for our culture’s exploitative and outdated “Caged Heat”-style excitement for the notion of women doing time together. As in “Weeds,” Kohan and her writers are obsessed with the million little details that form a believable and unembellished realm. Each episode contains fascinating revelations about the prison world, almost like a documentary report from within.

Orange Is the New Black

(13 episodes) is available for streaming at Netflix.com.