Jill Hennessy attends the Food Bank for New York City...

Jill Hennessy attends the Food Bank for New York City Can-Do Awards Dinner in Manhattan on April 16. Credit: Getty Images for Food Bank for New York City / Dia Dipasupil

Before Jill Hennessy became known for playing strong-willed women on TV—from attorney (“Law & Order”) to pathologist (“Crossing Jordan”) to spy (“Madam Secretary”)—she was a singer-songwriter, playing guitar for tips in a Toronto subway. And she’s still singing.

She serenaded cast and crew during breaks while shooting Showtime’s gritty new crime drama “City on a Hill.” Premiering June 16 and based on actual events, the series details a 1990s Boston investigation into citywide corruption, with Hennessy as a housewife married to a shifty FBI agent (Kevin Bacon).

Then there’s “Standing Up, Falling Down,” a new comedy starring Billy Crystal (shot in and around his native Long Beach), in which the two sing karaoke together. (The film does not yet have a release date.)

Hennessy, 50, raised in Canada, performed at My Father’s Place in Roslyn last fall. She owns 12 guitars, which are scattered throughout the Greenwich Village apartment she shares with her husband (real-estate entrepreneur Paolo Mastropietro) and their sons, Marco, 15, and Gianni, 11. She recently spoke with Newsday contributor Joseph V. Amodio.

This new series with Kevin Bacon looks intense.

Every script we get, I find myself gasping, “Oh, wow, they’re going there?” And “Kevin’s gonna do that? Okay….”  It’s some of the best writing I’ve seen. (Showrunner) Tom Fontana is one of the best in the business. They’ve created something at times disturbing, yet utterly relatable. They take characters who rob banks and do heinous things and make them incredibly sympathetic.

Like Kevin’s character.

He’s a corrupt FBI guy and I’m his devout Catholic wife trying to raise a 16-year-old daughter, and semi-aware that my husband is not the most kosher guy in the world. Episode by episode, she discovers things. And explodes. I had one of the most challenging, terrifying, wonderful acting days of my life last week, shooting a…physical, screaming scene. The director yells “Cut!” And I hear applause. The crew was actually applauding. That was a beautiful moment.

Nice. What I love about Kevin Bacon is his unpredictability—you never know what kind of character he’ll play next.

He’s one of the most professional people I’ve ever worked with. Such a gentleman. And he comes to play. He knows what he’s doing…and goes for it—takes chances. And…he looks great in any wardrobe.

You’re both rock musicians in your off hours.

That’s what’s great. I’m writing my third album, and I’ll say, “Hey, Kevin, I wrote a song, but one day I love it, the next I hate it.”

You should do a duet.

I would love to do a duet. That’s a great idea.

You also shot “Standing Up, Falling Down,” about a failed comic (Ben Schwartz) returning home to Long Island and winding up in a wacky relationship with his dermatologist (Billy Crystal).

Yes. (She laughs.) Just reading (the premise), I thought, I’m in. I play this crazy chick Billy meets at a karaoke bar. We end up singing karaoke…then my character finds out he—well, I shouldn’t give away the ending.

So you two actually sang?

Oh, yeah. We did a lot of takes, and let’s just say my throat was killing me. It was so much fun. Even the crew—we’re all singing at the top of our lungs. (She sings a lyric from a 1996 hit by technopop band Republica.) “Baby I’m ready to go-ohhh.”

How’s your new album going?

I’m hoping to tour ASAP, to try out these new songs before recording them—to feel where they want to go. Gauge audience reaction. Sometimes you learn more about the song by playing it out and hearing it. You learn what you’re trying to communicate.

Will you return to My Father’s Place?

I’d love to. That was a cool place to play. They’d just moved, so the venue itself was brand new. The original venue was older. A lot of the greats played there. People hold a special place in their heart for venues (like that) where they saw particular performers years ago. That’s how a venue gains a reputation, builds a following. It was kind of an honor to play out there. I also play (on the “City” set). It’s nice to bond with everybody in (a department like) hair and makeup, especially on a stressful day. It allows everybody to sit back, de-stress a bit. It’s a lot of fun.

Maybe you can sing on “City.” (At the time of the interview, Hennessy was still shooting episodes.) Would that work for your character—do you know where she’s headed?

Not really—and I kind of love that. Tom (Fontana) likes to keep things as a sort of surprise. You have indications. But I guess it’s just like life—sometimes things come at you fast!

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