All in the family.

The first question Liza Gennaro is invariably asked is, "Are you related to Peter Gennaro?" The answer, of course, is yes. She's his daughter, a chip off the old block if ever there was one. Liza's father is the veteran choreographerdancer of many musicals and TV shows. She's following in his footsteps with her first big Broadway production, the revival of the 1959 Once Upon a Mattress, starring Sarah Jessica Parker, which opened late last year.

Gennaro chatted about her father during a break backstage during rehearsals: "I studied jazz with him and assisted him on several shows, including the Three Penny Opera-the one with Sting. Working with him, I learned how to prepare, how to rehearse, how to clean up, how to look at a number and know it was wrong. I learned a technique." Her first big break was choreographing The Most Happy Fella, which moved from the Goodspeed Opera House to Broadway. "Gerald Gutierrez directed the show, and it was working with him that eventually led me to choreographing Mattress."

Life in showbiz began early for Gennaro, who danced as a kid on TV in the Milliken breakfast show. "My mother, who was a dancer, encouraged me to take classical ballet and jazz," she says. "Early on I was lucky enough to become one of the original members of Lee Theodore's American Dance Machine. That was a dance education in itself and a unique preparation for a choreographic career."

ADM's goal was to revive, restore, and perform routines from past musicals. She recalls, "We danced almost everything - Jack Cole reconstructions, Agnes de Mille dances taught by Gemze de Lappe. We worked firsthand with professionals like Buzz Miller and Gwen Verdon, assimilating their skills and performance styles. I was also lucky enough to work with Michael Kidd, but that was later during a stint with The Music Man."

Today Gennaro doesn't dance professionally (she's married and has a two-year-old daughter, Fiona). "Basically, I've always preferred being out front rather than performing onstage," she says, "though I'm very physical in the way I demonstrate what I want choreographically." She asserts with a laugh, "I make it a real workout!"

Gennaro believes that for any musical "the director-choreographer relationship is essential, and should be so seamless you can't see where the choreography begins and the director takes over. Gerry [Gutierrez] and I have always collaborated closely. Mattress is set in a medieval kingdom. We have eight dancers, four men, four women, and the same number of singers, plus the principals. Sarah, who plays the Princess, studied ballet and moves very well. With the character of the Jester, I tipped my hat to Dad, a song-and-dance man, in the way I choreographed it . . . this soft-shoe routine. Another number is what we call 'the Spanish panic' because there's so much running around. For that I studied gavottes, pavanes - and plenty of Carmen Amaya tapes."

No doubt if Mattress has a long run it will earn a place on that perennial satire, Forbidden Broadway, which pokes wicked fun at shows and the personalities in them. As its publicity is fond of pointing out, Forbidden Broadway in its twelve-years of various manifestations has outlasted many of the shows it lampoons. The latest version, Forbidden Broadway Strikes Back!, written and directed as always by Gerard Alessandrini, tilts at such hits as Show Boat (retitled Slow Boat: "They should cut somethin'/but they don't cut nothin' "), Miss Saigon (with a spoof set to There's a Small Hotel"), and Victor/victoria (a dead-on takeoff Julie Andrews snubbing the Tony Awards committee).

Choreographer Phillip George earns plenty of chuckles, too, especially from in-the-know dance followers. How, one asked, did George manage to get the essence of Susan Stroman's dances for Big, or Savion Glover, who he has frenziedly cavorting, in the takeoff of Bring in 'Da Noise, Bring in 'Da Funk? Says George, "Sometimes I have to see a show several times, but usually I go with first impressions - the first thing that strikes you about a routine and who's performing it. It's not always so hard after that, though I have to say I worked long and hard getting Bob Fosse's style right.

"With Savion, his style of tap isn't the style I'm used to. It's very valid, and his show tells a lot about the black history of tap, but it doesn't actually give you much on the other side - like you would never know there was a Paul Draper or a Fred Astaire. That's why I thought it would be fun to pair Savion, full of frantic energy, with Tommy Tune, the acme of soigne.

"With Big I think a lot of the humor comes from seeing adults pretending to be kids. With the Cats number, because it will surpass A Chorus Line as the longestrunning musical show in history, our four stars are given a Michael Bennett routine where the Singular Sensation' becomes 'Purr, purr, kick, scratch! / Oh, I've got a hairball in my throat!' "

Comic dance, believes George, is another pure theater form: "Humor's where my talent lies, and this edition of Forbidden has more dancing than any of the others. I've gotten such a kick out of doing it that I'm working on a comic revue called Cornyography. It's a history, going from the twenties through the nineties. No dialogue. It's like Bob Fosse's Dancin', only sent up-theater dance for comic effect. You know, rather like what P. D. Q. Bach does with music."

Meanwhile, the cabaret-sized theater, the Triad where Forbidden is playing, is attracting audiences and, occasionally, the very Broadway choreographers George is lampooning. "You know," he says wistfully, "I hope Susan Stroman comes to see it. I'm such a fan of hers."