Two men and a woman knocked on a door in Parsonage Road - in the Bath Road area - at 8.30pm on Monday 3rd March and having been allowed in, attacked the occupants, demanding money.
The offenders left after the police were called having stolen two mobile phones.
A 31-year-old man sustained serious head injuries which still require hospital treatment and a 45-year-old woman sustained a minor head injury.
Detective Sergeant Dave Colomb, of Bournemouth CID, said: “This was a vicious attack which left one of the victims with very nasty injuries.
“I urge anyone who has information about this incident or the offenders to contact Dorset Police as soon as possible.”
The first offender is described as a white man, approximately five feet eleven inches tall, of very slim build with pale skin. He was wearing a dark jacket with a lining that was possibly red in colour and a beanie hat.
The second man is white, of normal build with short red hair and a trimmed red beard. He was wearing was Puffa style dark coloured jacket.
The third offender, a white woman is approximately five feet five inches tall and of medium build. She was wearing jeans, a green jacket and short brown Ugg style boots.
No arrests have been made.
Witnesses and anyone with information should call Dorset Police in confidence on 101 quoting incident number 03:417. Alternatively, call the free and anonymous Crimestoppers line on 0800 555 111.