PBS, frequently treated as a doughty, vegetable supplement to the mild spice of network television and the red meat of cable lifted some eyebrows earlier this week with the announcement that the most recent season of “Downton Abbey,” the British period costume drama it imports, pulled in 13.2 million viewers per episode in its most recent season. In an age of attenuated ratings, that gives PBS a bona fide hit to challenge the post-apocalyptic road warriors of “The Walking Dead.”

This Sunday, PBS is launching the third season of the next show it hopes will grow from more modest ratings into a “Downton”-like hit, “Call The Midwife,” an adaptation of Jennifer Worth’s memoirs about working as a midwife in London’s East End during the introduction of the National Health Service. That series, along with “The Bletchley Circle,” which follows female code-breakers who return to civilian lives after World War II, and “The Last Tango In Halifax” are part of a strategy to make PBS a powerhouse on an already crowded Sunday night television schedule by appealing to an audience that gets little love elsewhere on the dial: women.

“We considered it to be somewhat of a market failure, and we’re always looking to fill those gaps,” said Beth Hoppe, the chief programming executive at PBS. “Our mission is to serve the audience where they aren’t being served. Cable and the networks all . . . define their audience 18 to 39 or 18 to 49 because they think they have the most buying power. We want to be there for all Americans.”

PBS’s Sunday night shows have a number of elements in common. First, they are intergenerational. On “Downton Abbey,” the Dowager Countess snipes at her American daughter-in-law and dotes on her granddaughters upstairs, while downstairs Mrs. Hughes mentors Anna and junior cook Daisy introduces her supervisor, Mrs. Patmore, to an electric mixer. A similar dynamic with a twist plays out on “Call The Midwife,” where the young midwives live and work with older nuns. The age gaps are smaller on “The Bletchley Circle,” but the women who worked together during the war and are drawn back to investigate crimes against women are at different stages of life, which is sometimes a source of dramatic tension. “That is something you don’t see a lot of,” Hoppe said, emphasizing that these shows have more than token female leads in mostly male casts. “Female buddy movies. Buddy series.”

And Hoppe noted that PBS shows strike a very different tone from the relentlessly grim interrogations of human nature that have gained such prominence on cable and garnered so many accolades. “It’s dirty and it’s difficult and there’s poor people and there’s crime, but it has so much optimism,” she said of “Call The Midwife,” which regularly interrogates the class and race prejudices of its characters. “These women bond together in the face of adversity.” “The Bletchley Circle is similarly blunt about the ways in which post-war Britain rejected the talents of the women who helped the Allies beat the Axis powers, even as it rejoices in the things they accomplish together, often beyond the notice of men.

There are improvements Hoppe would like to make, pointing to the influence PBS has been able to exert as a minority partner on British productions like “Downton Abbey” to encourage racial diversity in casting. And women are not her only targets: She cited her Wednesday night science-oriented lineup as a draw for male viewers, and pointed out that Henry Louis Gates Jr.’s recent mini-series “The African Americans: Many Rivers To Cross” reached 15 percent of African-American households, a staggering penetration for another under-served part of the American audience.

But when it comes to women, Hoppe is spurred by her success.

“I think the idea that mission and eyeballs are mutually exclusive is an idea that maybe comes from some of the men who run the commercial side. I just don’t think they have to be mutually exclusive,” she said. “I say we’re proving them wrong. It is not a truism that strong women aren’t what people want to watch on TV, because they’re watching it, and it’s leading to our success.”