March 04, 2016 09:45 AM

Sara Jaye Weiss/Startraks

Pregnant on the set!

They probably weren’t yelling that while filming this season of Gotham, but they sure could have been. Star Morena Baccarin, who’s expecting her first child with her costar, boyfriend Ben McKenzie, next week, was hard at work with her bump on display while filming.

“It will be a very true to life performance,” Baccarin, 36, tells PEOPLE of how her character Leslie is also pregnant this season, a plot line she says came about serendipitously.

“It was a total coincidence,” she explains in this week’s issue. “They were already planning on doing that with [Ben and my] characters when I got pregnant. When I told them they were like, ‘Okay, great!’ and I was like, ‘What?’ It worked out perfectly.”

Still, she had to go about hiding her bump in the beginning. “I was a little bit further along than the character at first so you’ll see me in a lot of jackets. They were very creative,” says Baccarin.

The cast and crew were also very accommodating. “They put chairs everywhere for me so that when we had a break, I wouldn’t have to walk more than a few feet to sit down,” she shares.

One colleague in particular — future father McKenzie! — had her back. “Ben’s the sweetest,” says Baccarin. “It’s very nice to work with your significant other, especially when you’re pregnant because you know you’ll get some extra TLC and get taken care of.”

One thing that was surely on his to-do list: getting her a Coke! “When I was at work I had to have a Coca-Cola,” says the former Homeland actress. “It got me through the exhaustion hump. Usually I hate soda and try to eat and drink healthy, but I was like, ‘You know what, if I drink a soda every day for nine months, it’s not going to kill me!’ “

But, thanks to McKenzie, 37, that wasn’t all she was drinking. “He was making sure I was drinking plenty of water and taking care of myself,” she adds.

Though Baccarin is already mom to 2-year-old son Julius, from her marriage to estranged husband Austin Chick, with whom she’s been locked in an intense custody battle for months, the new baby will be McKenzie’s first. “He’s very excited,” she says.

As he tells it, he’s ready for the good, the bad and the stinky. “[Being a father] is something I’ve wanted for a long time,” McKenzie told PEOPLE at the Gotham premiere on March 1. “I’m excited about all of it, poop, diapers and everything!”

For more on Morena Baccarin’s baby joy and drama, pick up the latest issue of PEOPLE, on newsstands now.

— Janine Rubenstein

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