“Family Guy” melds the best parts of Fox’s two biggest comedy hits into something new and improved.

The new animated series, a sneak preview of which will be shown after the Super Bowl on Sunday, melds the cartoon absurdity of “The Simpsons” with the outrageous dysfunction of “Married … with Children.” It’s guaranteed to offend almost everybody. Those who like their comedy subtle need not apply.

“Family Guy,” which returns to the Fox schedule in March, tells the story of the Rhode Island-based Griffin family. The head of the household is oafish Peter, who performs quality control for a toy manufacturer. His loving wife, Lois, provides stability to the family, which consists of whiny teen queen Meg, 13-year-old slug Chris and Machiavellian infant Stewie, who is scheming to take over the world. The brightest member of the family is Brian, the family dog.

In the debut episode, Peter gets fired from his job after falling asleep following a drinking binge at a stag party. Rather than admit being fired to Lois, Peter tries to cover things up. He applies for welfare, and because of a clerical error, is suddenly filthy rich. Lois eventually finds him out, and how he makes things up to her is a hoot.

The show’s comedy is firmly based in pop cultural references, in the machine-gun style of the Zucker-Abrahams-Zucker movies (“Airport,” “Top Secret”). In simple terms, throw everything at the screen and see what schticks. Even Fox itself is targeted in an extended Super Bowl scene. Tape this show, as it’s impossible to catch all the jokes in one sitting.

“Family Guy” is the brainchild of 25-year-old wunderkind Seth McFarlane, who produced, wrote, animated, directed and provided all the main male characters’ voices for the new series. In a few short years, McFarlane has gone from being a student at the Rhode Island School of Design to gaining a multi-million dollar development deal with Fox. Based on “Family Guy,” it’s money well spent.

McFarlane, coupled with executive producer David Zuckerman (“King of the Hill”), has given Fox the animated winner it’s been casting about for since the reign of “The Simpsons” began nine years ago. Don’t be surprised if the series eventually lands at 8:30 p.m. Sundays, behind Springfield’s favorite family.