That is largely how his casting has been received, though Hilton Als, the most prominent black critic in the American theater, found another dimension in it. He argued approvingly in The New Yorker that the production — which has a white Julie Jordan, played by the Tony winner Jessie Mueller — offers a rare instance of colorblind casting in which thought has been given to a black character’s presence in a largely white world.

Aside from his ensemble role in Green Day’s “American Idiot” in 2010, all of Mr. Henry’s Broadway roles until “Carousel” were written to be performed by men of color, often in stories about black culture — most recently “Shuffle Along,” in 2016, about the first black musical. After that, he spent 15 months playing Aaron Burr in “Hamilton,” in Chicago and then on tour, in San Francisco and Los Angeles.

He was playing Burr last summer when he and his wife found out she was pregnant. Suddenly “Dear Theodosia,” Burr’s tender pledge to his little girl, became a song that Mr. Henry was singing to his unborn child. A couple of times — on the lyric “I’ll do whatever it takes, I’ll make a million mistakes, I’ll make the world safe and sound for you” — his voice cracked with emotion onstage.

Early in the run of “Carousel,” he’d been singing to his unborn boy, too, tapping into his own anticipation to portray Billy’s in “Soliloquy.” As Samson’s due date approached, Mr. Henry’s castmates teased him, saying he’d never be able to sing it the same way again. The first time he had to perform it as a father, the day after the baby’s birth, he didn’t know how he would.

“I’d only gotten like two hours’ sleep,” he said. “You want to let go in the character, you want to let go emotionally, but I was concerned that if I did that, I would feel the actual feelings that I’m feeling in my —”