Graham Lockhart, 23, and Shauna Robb, 20, were killed in the crash along with children, two-year-old Tyler David, and 11-month-old Arianna Rose Sheryl.
The family, from Bathgate, West Lothian, was killed when their Fiat collided with an articulated lorry on the A801 near Polmont, on the outskirts of Falkirk, at about 2.20pm on Wednesday.
Tributes and flowers were laid at the scene yesterday.
As police renewed their call for witnesses, the families of the couple issued statements.
Relatives of Mr Lockhart said: "The Lockhart family are devastated at the loss of their son, daughter-in-law and two grandchildren."
Ms Robb's family said: "The Robb family are devastated at the loss of their daughter, her partner and their two grandchildren."
Tributes were also paid to the family on social media sites.
Sheryl Jones, Mr Lockhart's sister, said: "To have you ripped away from us is hard enough, but to have all four of you torn away is just crushing. Never felt such pain baby bro.
"I love the four of you with all my heart. My only comfort is you are all together.
"Wish use (sic) would all just walk through the door and this to be a horrible nightmare.
"You'll never understand how much we all loved you four."
Joanne Pirrie wrote: "Look after each other up there. R.I.P all four angels. Gone too soon. Will always be in our memories."
A friend of Mr Lockhart said: "Was just about to write something for you mate, just something to express how much of an amazing an inspirational guy you were to so many people."
Nicola Sweeney also paid tribute to Mr Lockhart and his family, saying: "Can't believe you are gone. God only takes the best."
Mr Lockhart's web page said he was a loft technician with an energy firm and that he studied law at the West of Scotland University.
The family's car had crossed into the path of oncoming traffic before the crash, which happened near the Lathallan roundabout by junction four of the M9.
Police want to contact the driver of a silver people carrier seen nearby before the accident. The lorry driver was badly shaken but not injured in the crash.
Sergeant Andrew Thomson, from Forth Valley Road Policing, said: "We are continuing our appeal for anyone who witnessed this tragic collision or who saw a black Fiat hatchback in the area before the incident at 2.20pm. We are particularly keen to trace the driver of a silver people carrier seen in the area before the crash."
The road, which runs from the Bowhouse roundabout near Maddiston to the roundabout that accesses Polmont and the M9, has been the scene of numerous accidents.
Two years ago Linlithgow and East Falkirk MP Michael Connarty spoke in Parliament about it being one of the most dangerous roads in Scotland.
He said that "if you don't know the area, the dip can be very deceptive".
The road was closed on Wednesday while police investigators surveyed the screened-off scene.