Fans of Alison Bechdel’s 2006 graphic memoir “Fun Home” know the title is a misnomer. During her fraught Pennsylvania childhood -- Alison's closeted father committed suicide four months after she came out to him as a lesbian -- “Fun Home” was the shorthand Alison and her brothers used for the family business, a funeral home.

With what’s being called “the first mainstream musical about a young lesbian," composer Jeanine Tesori (“Caroline, or Change”) and writer Lisa Kron (“Well”) have recast Bechdel’s novel for the stage. “Fun Home” has just been extended at the Public Theater through Nov. 17.

Under the direction of Sam Gold (“Seminar”), the rich adaptation moves forward at a whirling pace as we track Alison through three phases of life: awareness of her sexuality, fear of it, and the present. 

Alison’s growing self-acceptance unfolds in contrast to the downward spiral of her dad, who took liberties with his students (Bruce Bechdel also taught high school English) and finally, Alison suspects, took his own life by stepping in front of a truck. We’re meant to question the impact Alison’s coming out had on her father’s disintegration: “I didn’t know, Dad," Alison says at one squirm-worthy moment. "I had no way of knowing that my beginning would be your end.”

Broadway vets Michael Cerveris (“Evita,” etc.) and Judy Kuhn (whose great work this year has included the CSC’s “Passion”) are the familiar names in the “Fun Home” cast, as Bruce Bechdel and Alison’s fraying-at-the-seams mother, Helen. Our focus, though, is on the two women and one girl who play Alison at different stages. There’s adult “Alison” (Beth Malone), “Medium Alison” (Alexandra Socha) and “Small Alison” (Sydney Lucas).

Malone (seen on Broadway years ago in the Johnny Cash musical “Ring of Fire”), is the musical’s guide, the measured, if tough-to-read creator of the long-running comic “Dykes to Watch Out For.” As we jump back and forth in time, adult Alison appears in scenes with the two younger versions of herself. The intermission-less 100-minute story unfolds in non-linear fashion.

Tesori’s intricate melodies take hold from the opening, which has Cerveris lifting Lucas aloft like an airplane before the cast sings “Welcome to Our House on Maple Avenue,” a portrait of a nuclear family set to explode. Kron’s book and lyrics hit the right notes of sensitivity and sarcasm, particularly with a device adult Alison uses when she steps into moments of importance: “Caption,” she’ll say. “Dad goes out. Dad gets a newspaper. Dad goes cruising?”

David Zinn’s efficient turntable set and era-appropriate costumes serve the story well, and there's nice attention to detail, such as the "Chorus Line" Playbill brother Christian clutches on a dad-and-kids trip to the Big Apple, a journey meant to serve Bruce's ulterior motives.

There are, with “Fun Home,” a few things you’ve likely never seen depicted on stage. Chief among them is an 8-year-old singing about her first inklings of sexual awareness in the revelatory “Ring of Keys.” In that number, young actress Lucas sings longingly of the delivery woman she has just seen at the local diner: “Your short hair and your dungarees and your lace up boots / And your keys / Oh, your ring of keys.”

Socha, a veteran of Broadway’s “Spring Awakening,” also breaks ground as the 19-year-old college student who has for the first time bedded a woman (the talented Roberta Colindrez, as Joan). You vicariously share the thrill as Socha sings “Changing My Major”: “I am writing a thesis on Joan/It’s a cutting-edge field and my mind is blown.”

Scenes with the kids goofing around inside coffins at the Bechdel Family Funeral, and a fantasy sequence with the entire family morphing into a nifty facsimile of the Partridges, sequined costumes included, add to the production’s charm.

Lucas and Socha do a superb job capturing the emotions particular to Alison’s youthful circumstances. Griffin Birney and Noah Hinsdale contribute winning performances as Alison’s goofy brothers. Kuhn’s Helen is left largely unsketched. This is a father-daughter story, one that we know from its first moments will be tragicomic.

“Fun Home” is a clear and pointed reminder that you’re not truly an adult until you’ve understood your parents as flawed human beings. What’s left murky is what condition Alison finds herself in today. How did all this shape her ability to form close bonds? It would have been fascinating to walk away with a sharper sense of those issues. We can only guess how close to home that story would hit.

“Fun Home,” through Nov. 17 at The Public Theater, 425 Lafayette St. Tickets: $81.50 and up. Call 212-967-7555 or visit publictheater.org.

Follow Robert Kahn on Twitter@RobertKahn