Hilaria Baldwin has faced accusations that she fabricated Spanish roots and a Spanish accent

Alec Baldwin is supporting his wife Hilaria amid the recent controversy regarding her background.

Late last month, Hilaria, 37, began trending on Twitter as social media users — including journalist Tracie Morrissey and Twitter user @lenibriscoe — alleged that she has fabricated Spanish roots and a Spanish accent despite being born and raised in Boston, Massachusetts.

Through it all, however, the 30 Rock actor has stuck by his wife's side. "They celebrated New Year's in the Hamptons. While Hilaria has seemed a bit upset, Alec has been around to comfort her," an insider tells PEOPLE in this week’s issue. "He has been supportive and has tried to cheer her up."

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alec and hilaria baldwin
Hilaria and Alec Baldwin
| Credit: Patrick Mcmullan/Getty

Hilaria married Alec, 62, in 2012 and they share five kids together: sons Eduardo "Edu" Pao Lucas, 3 months, Romeo Alejandro David, 2, Leonardo Ángel Charles, 4, Rafael Thomas, 5, and 7-year-old daughter Carmen Gabriela.

She first addressed the controversy in a video posted to her social media on Dec. 27, confirming that she was born in Boston and her birth name is Hillary.

She explained that she occasionally "mixes" Spanish or English based on whichever she is speaking more frequently around that time and said that she "grew up spending time with my family between Massachusetts and Spain."

"This is just who I am and my life story," Hilaria said at the end of the clip. "It might not fit into your cookie-cutter and might not fit into a label, but it's my weird mix of who I am."

Alec and Hilaria Baldwin
Alec and Hilaria Baldwin
| Credit: Steven Ferdman/Getty

A friend close to Hilaria tells PEOPLE that the recent revelation is shocking. "She loves speaking about her Spanish heritage and seemed to want people to believe that she is Spanish," says the source.

"She wants the kids to know that they are half-Spanish. It's been important to her that the kids speak Spanish. And they all have Spanish names," adds the source.

Hilaria confirming that she was born in Boston is in contrast to what she has said in the past and what was previously listed on her Creative Artists Agency profile, which said she was born in Mallorca, Spain — where her parents now reside.

Additionally, as many on social media have pointed out, Hilaria has claimed she moved to the U.S. from Spain at age 19 to attend New York University in an April appearance on the #MomTruths podcast.

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Alec Baldwin and Hilaria Baldwin
Alec and Hilaria Baldwin in November 2019
| Credit: ANGELA WEISS/Getty Images

The Mom Brain podcast co-host has also frequently done media appearances speaking with a Spanish accent, including one on Today when she seemingly struggled to remember the English word “cucumber.”

She tried to further clarify the scandal in her video. "Yes, I am a white girl. Let’s be very clear that Europe has a lot of white people in there, and my family is white," she said. "Ethnically I’m a mix of many, many things; culturally I grew up with the two cultures. It’s really as simple as that."

Alec also defended his wife on Instagram last week, responding to one user who questioned her background in a comment on a post he made sharing a Mark Twain quote: "She was born in Boston but grew up in Spain. You got it?"