I scream, you scream, we all scream for . . . porn flicks?

Ben & Jerry’s sued a XXX-rated movie company yesterday for selling hard-core DVDs that spoof the famed ice-cream company’s labels and flavors.

Caballero Video’s “Ben & Cherry’s” line of smut features “titles and themes that are based on and deliberately trade upon” Ben & Jerry’s trademarks, court papers charge.

Examples cited in the Manhattan federal-court suit include the dirty movies “Boston Cream Thigh,” “Chocolate Fudge Babes” and “Peanut Butter D-Cup.”

Ben & Jerry’s says those titles are deliberate rip-offs of its “Boston Cream Pie,” “Chocolate Fudge Brownie” and “Peanut Butter Cup” flavors.

Even the company’s wildly popular “Cherry Garcia” got renamed “Hairy Garcia” for a series of fetish films featuring hirsute honeys.

And a flavor inspired by funnyman Stephen Colbert — “AmeriCone Dream” — became the gay-themed “Americone Cream,” with a cover featuring a photo of three obviously excited nude men.

Other flavors, including “Banana Split,” “Coconut Seven Layer Bar” and “Late Night Snack,” were turned into titles too filthy for publication in a family newspaper.

And while Ben & Jerry’s touts itself as “Vermont’s Finest,” the company says its “famous and distinctive” logo got twisted into “Porno’s Finest” on the DVD covers.

Other design elements allegedly lifted from the ice-cream company include its containers’ “large white puffy clouds,” “light blue sky,” “green grass” and “grazing cow.”

Court papers say a “side-by-side comparison” easily “evidences defendants’ blatant and outrageous copying and misappropriation of the Ben & Jerry’s intellectual property.”

They seek a court order directing that North Hollywood-based Caballero “deliver for destruction” all its allegedly infringing DVDs and related promotional materials.

Ben & Jerry’s is also demanding all of Caballero’s profits from peddling the prurient products, along with unspecified damages.

According to Ben & Jerry’s, Caballero’s abuse of its trademarks for “hard-core and exploitative” porn “is likely to cause confusion in the minds of consumers” who may mistakenly associate the skin flicks with Ben & Jerry’s wholesome treats.

Caballero execs Daniel Mamane and Tomer Yoffe, who are named as defendants in the suit, didn’t return a call for comment.