The setting in which married stage and screen stars Sebastian Arcelus and Stephanie J. Block were approached about joining the Broadway cast of Into the Woods was as perfect as the offer itself.

Tony Award winner Block and House of Cards and Madam Secretary alumnus Arcelus were performing on one of Seth Rudetsky’s Seth’s Big Fat Broadway Vacation cruises, traveling with their young daughter through the woods of Norway, when Block’s agent called. A replacement was apparently needed, in short order, for Sara Bareilles, who had originated the role of The Baker’s Wife in Lear deBessonet’s acclaimed revival of the Stephen Sondheim/James Lapine musical, which transferred to Broadway last summer after winning raves as part of New York City Center’s Encores! series.

“They said, ‘Look, you’re on a very short list,’” Block recalls. “‘Is this something you’d consider, and could you arrange all the moving parts in your life in a week or two?’ This sounds crazy — we were in Norway — but when you hear ‘Into the Woods’ and ‘The Baker’s Wife,’ you say yes. Then my agent said, ‘There’s also talk of Seb being cast as The Baker.’ That’s when you know you have to move mountains and do everything that needs to be done to say yes to this singular opportunity.”

Upon returning to the States, in fact, the California-based couple had to immediately find new living quarters. “We had to register our daughter in a different school here on the East Coast, rent a house sight unseen, furnish it in four days, and rehearse the show in just a handful of days,” Block says. “It has been a joyful, sort of psychotic whirlwind” — an adventure, to be sure, if not as perilous as the one they’re now enacting on the stage of the St. James Theatre, where Woods is playing through January 8.

Block and Arcelus had played husband and wife before, on Madam Secretary, though as Arcelus points out, “Our relationship was on the outs, sadly.” (“In the show, not in real life,” Block clarifies.) Patina Miller, who currently plays The Witch on Friday and weekend performances of Woods, played a principal role in all six seasons of the TV series and remains a “dear friend,” Arcelus says, despite the tension between their characters in the musical.

“The reality is, with a show like this, which is so beautifully complicated, if you decide at any moment that you can relax — if you think, ‘OK, I have it’ — something will happen to turn you upside down,” Arcelus notes.

“There’s no coasting with Sondheim,” Block agrees.

The Baker’s Wife had been on Block’s bucket list since she received a copy of the original cast recording as a 16th birthday present. “I thought, ‘One day I’m going to play this role.’ I didn’t know it would be thirtysomething years later. And this is my very first Sondheim show! I’ve never done a Sondheim production. I would always say to Sebastian, ‘I don’t know how one makes a living in this industry and loves this art form as much as I do without ever having done a Sondheim piece.’”

She adds, “For it to happen now — sadly, after his passing — and to have such a close relationship with James Lapine,” Block’s director in productions of Falsettos and Little Miss Sunshine, “and for James to have seen the show and given the cast our blessing, it’s really been a lovely, lovely experience.”

Arcelus actually played The Baker in a college production of Woods as a senior at Williams College, also Sondheim’s alma mater. “It was at that point in my life a very cathartic event. I was a political science major, and as a senior I decided I would pursue a career in acting after college, so it was a springboard for really embracing that life.”

In the musical, Arcelus and Block’s characters are driven into the woods in order to reverse a curse, placed by The Witch, barring The Baker from having children. DeBessonet, who recently gave birth to a daughter, was “nine months pregnant when we started rehearsals,” Arcelus points out, “and she showed up every day, and was so giving and so present for the company, and for new actors joining the process.”

The result, Block says, was “a life-affirming space” in which “every day a lyric or a scene or a new actor would bring something different. It was so special to create with her and beside her. I find that to be the case with Into the Woods, though. People are walking away talking about how they’d heard one particular song a thousand times but never that same way, or how they’d never understood that one line before seeing this production. And that’s not just about the performances. The magic is that the material is the star of the show.”

Arcelus concurs. “It’s amazing that you can have a piece of theater that’s so iconic, and yet when it’s presented again it becomes a new, personal experience,” he says. “Doing the show now, at my age, married to this extraordinary woman and trying to raise an extraordinary child, it resonates in a different way than it did when I was in college. It came back into my life at the perfect time.”