Picture it: A dad strolls down Main Street. His wide-eyed, 10-month-old daughter, perched in her stroller, giggles and coos. It’s a fall day—not too hot, not too cold. Yet a stranger stops the dad, asking if he thinks that baby could use a hat. No, she couldn’t, he replies, mustering a perfunctory smile. Dad keeps walking but is stopped by yet another passerby who urges him to return home at once, as it is much too cold out for a baby. Then, still another concerned citizen sidles up to serve up a scolding.

Having reached the end of his tether, the dad briefly entertains telling this latest busybody to butt out—but he stops himself. Little ears are listening, after all. Instead, he reassures the concerned (meddling?) lady that his baby is in good hands. This, even though nobody on Main Street—or Madison Avenue—seems to believe him.

When it comes to their talents and abilities at raising children, or handling virtually anything having to do with the household, dads are feeling a lack of respect. A report this past March from PR firm Edelman and The Parenting Group, publisher of Parenting and Babytalk, found that 66 percent of fathers think there is an “anti-dad societal bias.” Among dads with children under the age of 2, that number spikes to 82 percent.

One need to look no further than a controversial diaper ad to see their point.

When Huggies’ “Dad Test” campaign, featuring flummoxed fathers attempting to care for their newborns, hit the airwaves, dads decided enough was enough. The backlash was swift, and a wave of negative reaction stained the brand’s Facebook page like spit-up on a cashmere cardigan. One faction of fathers even teamed with Change.org to petition Huggies parent Kimberly-Clark Corp. to stop running ads portraying dads as incompetent.

It is clear that the fathers of today want the world to know they have moved beyond the stereotypical image of the “doofus dad.” They want to be seen as nap time ninjas, professional purveyors of PB&J and diaper-wielding demigods—ones who also happen to shop for those diapers.

Huggies executives listened and attempted to clean up the mess by withdrawing the dad-bashing ads. What’s more, brand representatives trekked to the Dad 2.0 Conference in Austin, Texas, this past March. Jeremy Adam Smith, author of The Daddy Shift: How Stay-at-Home Dads, Breadwinning Moms and Shared Parenting Are Transforming the American Family, was also at the gathering and met with Huggies reps there. “If they are hoping to sell diapers to dads, that was that group to talk to: dads who write, who blog about fatherhood,” he says. “What struck me was they really didn’t know—it just hadn’t occurred to them” that the ads would be offensive.

Not everyone believes Huggies’ full-court-press PR play was the right move, however. “I’m surprised that they caved,” says Hayes Roth, CMO at Landor Associates, a brand consulting and design firm. “[Huggies] had this golden opportunity. Instead of withdrawing [the ads] and rushing down [to the conference] to apologize, why didn’t they do something with social media, [such as] ask people to vote: ‘Do you like the ads or do you find them offensive?’ Start a dialogue.”

The fact is, a dialogue was started—and as evidenced by this story, it is still going on. But beyond protesting stereotypes, the next obvious question seems to be: How does the dad of today want to see himself portrayed in ads? After all, the image of the modern father as some sort of superman—one hand on the push mower, the other on the baby carriage—would seem merely a stereotype of a different stripe.

“Advertising is a form of art. Art is only good as long as it reflects the truth—especially our kind of art, where we are trying to do art that persuades,” says Bruce Jacobson, associate creative director at Y&R New York. “The best ads come up with that kernel of truth that is going to resonate with the person seeing it.”

So what is the truth of the modern dad? Says Smith: “More men are saying being an involved caregiver, even if you are the breadwinner, makes life more meaningful—which sounds warm and fuzzy, but also has very specific implications for the economy and the marketplace.”

Naturally, there are as many varieties of the modern American dad as there are of, well, the modern American mom. Some dads (and moms) are primary caretakers, others aren’t. Some work outside the home, others do not. The garden-variety parent, regardless of gender, suffers from sleep deprivation, wrangles pickups for play dates and hopelessly dodges pointy little plastic things strewn across the kitchen floor that, when stepped on, hurt like all hell. (The evolution of the dad, and mom, in marketing messages extends to same-sex couples as well. Consider the dustup earlier this year when JCPenney was threatened with a boycott by a group called One Million Moms for including a lesbian couple and their kids in its catalog. The retailer responded by creating a Father’s Day-focused ad featuring real-life same-sex couple Todd Koch and Cooper Smith playing with their children, Claire and Mason. “What makes Dad so cool?” went the copy. “He’s the swim coach, tent maker, best friend, bike fixer and hug giver—all rolled into one. Or two.”)

And dad is no longer just the fixer—he’s also every bit the consumer. According to a Yahoo survey of 1,000 dads last year, the influence of dads in deciding which consumer goods are brought into the home is growing, with 57 percent of those polled saying they are the primary decision maker, another 37 percent indicating they share the responsibility with a partner.

But even with dads participating in domestic life much more than their fathers ever did, many marketers still struggle to figure out how to reach them. What’s certain is that advertisers cannot rely on what’s worked in the past. Just think about those commercials for laundry detergent in the 1970s. Where was dad? Nowhere—and for good reason. He wasn’t the target audience. Mom was the caretaker, and she, it was understood, made household purchase decisions.

If dad was seen at all, he was a prop—coming home from work to admire the fruits of the missus slaving away, or else as some bumbling, hapless character. Archaic as that sounds, it was a smart marketing strategy. “The image of male domestic incompetence has long been an effective selling tool because the marketing target was women, who liked that image or at least identified with it,” explains Donald N.S. Unger, a lecturer at MIT and author of Men Can: The Changing Image and Reality of Fatherhood in America. “When patriarchal power was more monolithic, those ads had the character of making fun of the powerful.”

But as the family dynamic has changed, with more women becoming educated and entering the workforce and men sharing more of the load at home, the doofus dad—an increasingly extinct figure in the culture—nonetheless has remained a fixture in some ad campaigns. Same goes for prime-time TV. (Consider Ty Burrell’s hapless Phil Dunphy on ABC’s hit Modern Family, or Will Arnett’s clueless Chris Brinkley on NBC sitcom Up All Night.) A turning point was the recent global economic meltdown, dubbed the “mancession” because of the perception that men lost jobs at a faster rate than women. As a result, more dads suddenly found themselves at home with the kids, and along with a shift in the family structure came a shift in society’s view on dads.

“The economic landscape, where women under 30 make more than men, has made serious inroads in the domestic sphere in recent years,” says Unger. “Younger people are rewriting their domestic scripts along looser, more personalized, more functionalist lines, forming domestic arrangements that fit their beliefs and circumstances rather than traditional patterns.”

All that meant that marketers were forced to rethink the images they were putting out there. “If it’s something that people recognize about himself or herself, then they are willing to grin and bear it, but not if they recognize it’s a stereotype that is somewhat insulting,” says Robert Passikoff, founder and president of Brand Keys, a brand consultancy whose clients include Procter & Gamble, Papa John’s Pizza and the U.S. Army. “Gender becomes less the issue, and authentic and engaging portrayal becomes the mandate.”

As Huggies learned, the stereotype of the incompetent parent isn’t likely to resonate with dads—or for that matter, moms. “A female physician, attorney or business exec whose domestic deal is that she’s the breadwinner and her husband is the homemaker is much less likely to find the doofus dad image funny,” says Unger. “That would suggest that her children are not safe with their father, that she had been irresponsible in ceding them to his care.”

There are other recent campaigns featuring dads that have been pitch perfect. DDB London’s tug-at-the-heartstrings spot for the Volkswagen Polo takes the consumer on a father’s lifelong journey to keep his daughter safe—taking her to swimming lessons, greeting her first date at the front door and, finally, sending her off to college in a car deemed safe enough for his precious cargo. A similarly themed spot, also from Volkswagen, features a guy across different stages of life whose sole concern, whether shopping for a bike or a car, is how fast it goes. That’s till the final shot, when we see him checking out the VW Jetta with a newborn strapped to his chest, wondering only, “Is it safe?”

The image of the capable father is also showing up more in CPG marketing. Procter & Gamble paired the modern dad with a celebrity pitchman in a campaign from Publicis New York for Vicks VapoRub featuring New Orleans Saints star quarterback Drew Brees. In the spot, we see Brees applying the healing salve to the chest of his real-life son, Baylen, before crashing with the kid in his twin bed for keeping watch through the night. Dad as MVP has been quite the successful play for Kelloggs Co. as well. Its campaign for Frosted Flakes features the line, “Share what you love with who you love,” and sports images of dads playing sports with their kids and brand mascot Tony the Tiger.

In their messaging, brands must be sensitive to the roles—and self-image—of both moms and dads. In its study, Edelman found that each parent perceives he or she does more of the grocery shopping, with 70 percent of dads maintaining they commandeer the Trader Joe’s cart while only 36 percent of moms agree. Thus, marketers are faced with the task of balancing messaging to both moms and dads—which can be a tough trick to pull off. “There is a much more egalitarian awareness, which is great,” says Hayes. “But you have to be about something. You just can’t be everything to everybody. No brand can do that effectively.”

Eric Weisberg, executive creative director at JWT New York, says it is all about striking a balance. “Even 10 years ago, we were mainly talking to moms,” he says. “Now there has been a shift. Mom remains core to the strategies, but we’re talking to dads to be sure we are good with them too.”

Jacobson agrees. “You have to say, OK, you know what? This is a little bit of a shift,” he says. “Our target used to be mom. Now, maybe it’s dad. So let’s try to come up with stuff that is going to jibe with his reality.”

And much of that reality still has dad strolling down Main Street, getting unwanted advice at every turn from well-meaning but misguided passersby. This Father’s Day, there’s little doubt that what the modern dad wants rather than that “No. 1 Dad” mug or burnt toast is a little respect.