There’s an in-joke at the beginning of Alfonso Cuaron’s film “Y Tu Mama Tambien” that I completely missed the first couple of times I saw it. Understandable, maybe, since the scene has Tenoch (Diego Luna) and his girlfriend engaging in some fairly enthusisatic sex in her bedroom. (The film was quite an arthouse hit back in 2000, and a controversial one; I remember one older couple telling me they lasted 10 minutes before the on-screen sex sent them packing.

But on the wall of the bedroom behind the couple is a gigantic Spanish-language movie poster for Hal Ashby’s “Harold and Maude.” That’s a sly wink to the older woman-younger man (or men) romance to come in “Y Tu Mama Tambien.” But it’s also a clue that Cuaron has a lot more on his mind here than a fun sex romp. This is a sex romp with layers, layers that even the characters often are oblivious too, and the brilliant thing about the film is the way it suggests those layers while still often being a fun, buzzy, sexy film. “Y Tu Mama Tambien” is now out this week in a stellar new Blu-ray/DVD combo pack from the Criterion Collection.

The film made stars out of Luna and Gael Garcia Bernal (Julio), who play typically horny, gross, lovable teenage boys, both bored after their girlfriends go to Europe. On a whim, they invite an older Spanish woman (Maribel Verdu). For reasons that aren’t immediately clear, she accepts, and the threesome hit the road in an old station wagon, blasting tunes, smoking weed and talking about sex. Along the way, Luisa will seduce them both (in two sloppy, funny, brief scenes that belong in the Bad Sex pantheon) and a combination of lust, jealousy, fear and simple inexperience starts eroding the foundation of Tenoch and Julio’s friendship.

In making “Y Tu Mama,” Cuaron was returning to his native Mexico City after a couple of successful forays into Hollywood, including the 1998 “Great Expectations” with Robert De Niro. (His biggest triumphs, including “Children of Men,” were still years away.) And the film does have a loose, “one for me” feel, shot with handheld cameras as if Cuaron was the fourth person in the station wagon.

But that casualness can be deceptive, and rewatching the movie I was struck how many truly beautifully-composed shots Cuaron gets in there, including several of his trademark long takes (here used to suggest a naturalness in the trio’s interactions) and some stunning compositions. The scene of Tenoch and Julio swimming naked in a leaf-covered swimming pool, their boyish bodies cutting through a perfect blue beneath the jagged dark red of the leaves, is fantastic. Cuaron is having a good time, but he’s not slumming.

The casualness can also distract from the psychological acuity of the characterizations — one of the extras on the Criterion DVD are detailed character studies, short stories really, that Cuaron and his brother, co-writer Carlos Cuaron, wrote for each of the characters. These people are a lot deeper than we initially see them for — especially Luisa, whose reasons for taking the trip don’t become clear until the end of the film (but in retrospect, are right there in front of us.) But also Tenoch and Julio are revealed to be more than just horndog teens — under their bravado, they’re insecure and uncertain, and unaware of how their different social classes (Tenoch’s family is rich, Julio’s isn’t) will come to undermine their friendship as they enter adulthood.

One of the key ways the film suggests those depths is through the use of repeated voiceover narration, which often sounds like an audiobook, giving us information about the characters’ histories, and the memories they carry with them. The omniscient narrator will also tell us what happened, or what will happen, to a minor character the travelers meet on the road, such as the happy fisherman and his family they meet on the beach. In two years, the film tells us, he’ll be a janitor at a hotel, a casualty of globalization. The characters, of course, move through life oblivious to all this — a technique that also occurs in some background visuals as well, such as when we see police officers raid some roadside protesters as the station wagon whizzes by.

Having these political, economic, and psychological forces swirling around the film makes its simple story, a pilgrimage of three people to the beach for a good time, feel more fragile and poignant somehow. We know the good times can’t last, but “Y Tu Mama Tambien” reminds us of that while the good times are actually happening. Joy is fleeting and the future is unwritten. Especially for two young, dumb, beautiful boys.