ET reported in January that the couple and their family are "very upset" that Hilaria's identity and background "are being questioned," following social media claims that she exaggerated her connection to Spain.
"Hilaria is such a soft-spoken, kind, caring and loving person, and the harassment and hate that she has been receiving on social media has been a lot for her," the source said, adding that the controversy has "deeply affected" her and her family.
"Alec has always known that Hilaria is from Boston," added the source. "Alec unconditionally supports and loves Hilaria in whatever she does and this situation has been no exception. They are focused on taking care of their small five children and being there for each other as a family."