"It was inside of the rim of my frappuccino," she added.
"My wife and my baby just drank someone's blood," her husband Louis told KTLA. "It was bad."
The family called the Starbucks to report the incident and an employee told them that one of the baristas had been bleeding earlier and was taken off the floor.
The manager at first offered the family free drinks for a week, and said that the barista would get tested to make sure he or she didn't have HIV or any other kind of blood borne disease.
But the family later learned that the employee was never forced to get tested, so they had to test themselves.
"We felt sick to our stomachs, we shouldn't have to worry about going to get something to drink and there being blood in our drink where we could get sick," Mrs Vice said. "It's very stressful."
The first test came back negative, but they had to do another one six months later to make sure they were clean.
"This caused the family stress, nervousness, fright, anguish, grief, anxiety, worry and shock for several months while awaiting the second round of test results," their lawyers said.
The second tests came back negative as well.
Starbucks later upped their offer to $1,000 (NZD $1,378) for each family member who drank a tainted drink, but the Vices say that won't cut it.
"I thought it was sort of belittling," Mrs Vice says now of the offer.
The family is now suing for unspecified damages.
When contacted by local news outlets about the case, Starbucks refused to answer any specific questions but released this statement:
"We are aware of this claim that allegedly took place in 2016, and are prepared to present our case in court."