The crash happened at the A165 junction with Grindale Road, near the villages of Buckton and Bempton, at 3.30pm on Friday May 7.
The Peugeot had struck a Mercedes GLA.
The driver and passenger of the Peugeot, a man and a woman in their 30s, sustained fatal injuries and died at the scene. A child travelling in their car was taken to hospital as a precaution and suffered minor injuries. The families of the deceased are being supported by specially trained officers.
The female driver and sole occupant of the Mercedes sustained serious injuries and was taken to hospital for treatment, where she remains in a serious condition.
Humberside Police are appealing for anyone who saw the collision or either vehicle prior to the collision to contact the force on 101 quoting log 338 of 7 May 2021.