ABC Family President Paul Lee believes the cable channel, which is owned by Walt Disney, hasn’t strayed from its “family” name despite the racy plot lines of its shows.

Hollywood ? The TV series “The Secret Life of the American Teenager” opens with a 15-year-old girl coming home from band practice, reaching into her French horn case and pulling out a home pregnancy test. Her horrified look confirms the results.

No less startled are some parents whose children have watched the ABC Family cable program that revolves around the sex lives of high school students. The titillating themes, in their view, are out of place on a channel with the word “family” in its name — especially given the chaste image of its owner, Walt Disney Co.

But “Secret Life” has become ABC Family’s biggest hit and one of the most popular shows on cable, drawing an average of 3.8 million viewers an episode. With depictions of teens rolling out of bed, a father peppering his daughters with questions about their sex lives at the dinner table and a troubled boy revealing that he was molested by his father, “Secret Life” represents a coming of age for a channel founded by evangelist Pat Robertson to spread the Gospel.

Welcome to Disney’s new take on the American family.

Along with shows such as “Greek,” set in the belly-shots-and-wet-T-shirts world of college fraternities and sororities, and “Lincoln Heights,” a drama about growing up fast in a crime-ridden Los Angeles neighborhood, Disney says it has reshaped ABC Family into a channel more in sync with the realities and anxieties facing many American families and teenagers.

The programming ethos will take another twist in March, when ABC Family debuts “Sophie,” a comedy series featuring a young woman who has everything she wanted, including a loving boyfriend and a baby on the way. That is, until the guy dumps her.

ABC Family’s strategy casts a new light on the traditional Disney brand, which historically has mined such tales of youthful innocence as “The Little Mermaid” and “The Parent Trap” to win over generations of viewers. The approach has paid off. ABC Family’s ad revenue and ratings have been on the rise, making 2008 its best year.

“The best way to resonate with your audience is to be authentic,” said Anne Sweeney, president of Disney-ABC Television Group. “And you’re only authentic if you are holding up a mirror to your audience and saying, ‘I see you.’ “

Disney’s quest for authenticity, however, has sparked debate about what constitutes “family programming” and how far the most influential family-entertainment company can push boundaries.

Disney executives have wrestled for years to find the right formula that is faithful to its “family” name but also appeals to younger viewers who have outgrown the perky adolescent worlds depicted in standard teen-targeted shows such as “Hannah Montana” and “Wizards of Waverly Place.”

An internal ABC Family study that surveyed the attitudes of so-called Millennials — viewers ages 12 to 30 — found that they craved strong relationships with their families and friends. Those results partly influenced the decision by the channel’s management team to recast the cable network as “a new kind of family.”

“We set out to make the modern family in all its passion and dysfunction, and reclaim that word for what it really is for our audience,” ABC Family President Paul Lee said.

Although ABC Family targets the 18- to 34-year-old demographic, one-third of “Secret Life” viewers are 12 to 17. The programming makeover has left some parents worried that ABC Family is sending younger viewers mixed messages about healthy behavior — and inadvertently encouraging teen sex and underage drinking.

“I thought it was going to be more like Disney Channel, a little more grown-up but less provocative,” said Mary Alden, a Los Angeles-area mother of 14-year-old twins. She became alarmed when she heard dialogue from characters in “Secret Life” who were discussing whether one of them should end her pregnancy. “I didn’t think that would be on a Disney channel,” she said.

Michele MacNeal, a mother of three who also lives in the Los Angeles area and heads a local branch of the watchdog group Parents Television Council, agreed.

“It’s kind of a misnomer to call ABC Family a family channel,” she said. “When you call something ‘family,’ it gives the impression that it’s safe for all members of the family, even young children.”

Originally launched as part of Robertson’s Christian Broadcasting Network, the channel still airs “The 700 Club,” a Christian-perspective news and talk show. Redubbed “The Family Channel” a decade later, the name struck a chord in the “family values” political campaigns of the 1980s.

In 2001, former Disney Chief Executive Michael Eisner, looking to expand in cable television, agreed to pay $5.3 billion for the channel.

Sweeney, who had been running the Disney Channel, was put in charge of ABC Family in 2003. Her first priority was to differentiate the channel’s programming so that ABC Family and Disney Channel each had a defined audience and didn’t poach the other’s viewers. She reached outside the close-knit Disney organization to find a day-to-day manager of ABC Family and picked Lee, a former BBC America executive.