A family court judge said the woman had a "more relaxed" parenting style but the man was "firmer".
Judge Ross Duggan said the woman talked about "irreconcilable differences of parenting style" and told of "frequent arguments".
He said the couple offered a "hopelessly unstable family life".
The judge has approved a social workers' plan which will see five children aged between 13 and five live in foster care and a toddler placed for adoption.
Detail of the case has emerged in a ruling by the judge following a private family court hearing in Leyland, Lancashire.
Judge Duggan said the family could not be identified but said the local authority involved was Lancashire County Council.
He indicated that the woman was the mother of all six children but the man was not the father of all six.
"The parents had a fundamental disagreement over parenting, father being firmer, mother being more relaxed, and this no doubt contributed to the disagreements, turbulence and worse in their home," said the judge.
"I am driven to conclude that a child in their joint care would be exposed to a turbulent home life, a life with domestic abuse, a life with anger, a life which would probably involve separations and reconciliations, a life which would involve uncertainty so far as accommodation arrangements are concerned."
He went on: "(The mother) has spoken of irreconcilable differences of parenting style. She has spoken about frequent arguments and a pattern of domestic abuse."