Felipe and Iris Rodriguez had been married 14 years and leave behind a 13-year-old daughter, Samantha, Barahona said. The couple's daughter was at school at the time of the shootings, she said.
Family members were gathered at the home of Iris Rodriguez's parents in Salt Lake City trying to make sense of what had happened, Barahona said. The couple had dinner on Thursday with family and did not appear to be having problems, nor was family aware of any unusual financial pressures, she said.
"Iris was a very happy person, very loving, very caring," said Barahona. "Felipe we know as her husband, and he was also always very happy. He didn't seem to me like he would do something like this."
Police have provided few details about the shooting. and a motive for the incident remained unclear Friday night.
UHP Cpl. Todd Johnson said troopers found the SUV off the side of the highway underneath an intersecting Interstate 215 overpass, not far from Salt Lake City International Airport.
"There are two dead adults, the female driver and a male passenger. Both appear to have gunshot wounds to the head, so we're looking at this as a possible murder-suicide," Johnson said Friday morning.
Johnson said there was no crash involved, as had been reported earlier.
The incident closed down the eastbound I-80 ramp at Redwood Road, as well as the I-215 westbound exit to eastbound I-80, until 3:30 p.m.
UHP has released the couple's bodies to the state medical examiner's office for autopsies.
Bob Mims and Michael McFall contributed to this story.