Skye Tavis Buck, 30, and his pregnant wife Courtney Elizabeth Buck, 30, are both missing and presumed dead, say police.
The couple apparently lost control of their vehicle on the icy highway and skidded down a 30-metre embankment, striking a tree before disappearing into the river, say police.
Attempts to find the vehicle on Sunday night were unsuccessful and dive teams and search and rescue teams resumed the search on Monday, but the vehicle has not yet been located.
The pair taught at Clearwater Secondary School and at Raft River Elementary School. Courtney Buck was seven or eight months pregnant, members of the community told CBC News.
With a population of just 5,000, the teachers' deaths have had a significant impact on the people of Clearwater, says Michael Bowden, principal at Raft River Elementary.
"The community is reeling and so is the staff and we're just trying to make sure that our staff and our kids are taken care of here at the school," said Bowden.
Bowden says a school district trauma team is at the elementary school to support the children and staff members.
Sean Garvey remembers his former basketball teammate, Skye Buck, as a generous friend.
"Skye was the best. I mean, in every sense of the word. What he stood for, who he was, how he treated everybody around him."
The accident victims were both 30 years old, and expecting their first child.
"They were absolutely the perfect couple. The exact same people. So caring, so giving, so wonderful, just wonderful," Garvey said.