It's a hot August day in Los Angeles, yet a heavily pregnant Morena Baccarin has broken off from filming Homeland's third season to give an interview. It's testament to the 34-year-old's grace and poise that she has done so without breaking a sweat, immaculately made-up and resplendent in a deep blue dress and heels, her sole concession to her condition being the more-regular-than-usual bathroom breaks.

This is the sort of adversity to which Baccarin's Homeland character, Jessica Brody, has grown accustomed. The show's tangled terror storyline climaxed at the close of the last series with Jessica's husband Nicholas Brody (Damian Lewis) on the lam, suspected of blowing up half the staff of the CIA. There were victims, and then there was collateral damage: at the start of this new series, the Brody family is just barely holding it together in the eye of an angry media storm.

While she may have spent most of the show's early episodes cooking, crying, and looking vaguely concerned, Jessica grew in stature during its second run, as her husband, returned and apparently recovered from his eight-year stint in captivity, became a vice presidential candidate – and she a prospective Second Lady. Safe to say that side of Jess has been put away for season three, though it did earn Baccarin her first nomination for an Emmy in the Best Supporting Actress (Drama) category (she lost out to Breaking Bad's Anna Gunn).

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Baccarin herself is somewhat more happily married than her screen alter ego, and tied the knot with writer-director Austin Chick in 2011. She's due to give birth to the couple's first child around the same time as the new series debuts on American TV on 29 September. When she broke the news of her pregnancy to Homeland creators Howard Gordon and Alex Gansa, she was confident they'd be cool with it – after all, her co-star Claire Danes was pregnant during season two.

As for disguising her condition on screen, she says, "It's all done in post-production … I certainly didn't have to carry around laundry baskets for the entire season."

Baccarin's baby will come from a long line of theatricals. The actress's great-uncle is a celebrated Brazilian director. Her late uncle, Ivan Setta, was well known for playing screen villains in his home country. Her mother Vera is an actress, who in 1976 appeared as a vampire named 'Morena' in the film O Vampiro de Copacabana ('The Vampire of Copacabana'). Three years later, her daughter was born in Rio.

"My mum … tells me so many different versions of how I got my name that I never know when she's telling the truth. She's an actor – so she lies a lot."

Baccarin grew up speaking Portuguese, but learnt English from the age of seven and speaks without a hint of an accent. Yet early in her career she was pigeonholed as a Hispanic actress and locked out of many roles as a result.

Today, the highest-paid actress on American television is Colombian Sofia Vergara – but, says Baccarin, "Ten years ago you would rarely see an ethnic person in any lead role, unless that role was explicitly ethnic – say, Jennifer Lopez playing a Hispanic character. In fact, when Jennifer Lopez started to play regular women in romantic comedies, she really helped the industry to catch up with the rest of the world."

When she was 10, Baccarin's father, Fernando Baccarin, an Italian TV news editor, was offered a job in New York, and the family relocated to the West Village. At the New York City Lab School for performing arts, one of her classmates was a future colleague: Claire Danes. "At the beginning, let me tell you, I was rough – I was not a natural talent like Claire."

Baccarin's first TV appearance came in 2002, when she landed a part in Joss Whedon's cult sci-fi drama Firefly, which lasted just one season but has lived on as a fanboy's favourite ever since.

Following Firefly, Baccarin became known as a sci-fi specialist, and featured in the recent, now-defunct remake of the 1980s series, V. Her experience on both those shows made Baccarin a regular visitor to the annual Comic-Con convention, and prepared her for the sort of fan fixation she has latterly experienced with Homeland.

"Sci-fi fans are a different breed," she says. "They are so loyal, it's unbelievable. They've seen every sci-fi thing I've done and then they started watching Homeland because I was in it."

Nowadays, of course, everyone is a TV geek, and few shows inspire quite as much frenzied web conversation as Homeland. Not for the first time, Baccarin won the role of Jessica after another performer proved unsuitable. The pilot had to be re-shot to include her.

In fact, she experienced Homeland first as a fan. "I watched a trailer and was riveted," Baccarin says. "V had just been cancelled, I was looking for a job and the Homeland script came across my desk. I loved it immediately, although I thought it would end up being discovered gradually – a slow-burner, like The Wire." No such luck.

Series 3 of 'Homeland' begins on Channel 4 on 6 October