The party's policy chief Jon Cruddas said women felt a "deep feeling of unfairness" at being expected to work, look after children and care for elderly relatives as they increasingly took on the role of breadwinner.
The solution was a "whole family" approach to public services, the MP leading the Opposition's policy review said, based on an assumption children "need a relationship with both parents".
In a speech to the Civitas think-tank, Mr Cruddas warned against the risk of all fathers being seen as a "potential risk" because of the "sexual violence of a few men".
"Families thrive when there is a partnership and teamwork amongst adult relations," he said.
"But there is a deep feeling of unfairness amongst women at the burden they have to shoulder.
"Too many have a triple shift of paid work, looking after the children and caring for an older relative.
"Amongst men, there is the sense of being excluded from domestic life.
"We need a new conversation about families and their relationships that is jointly owned by women and men.
"We need to value father's family role as highly as his working role, and women's working role as highly as her domestic one.
"And we need to have high expectations of fathers because otherwise we collude with those men who don't step up to the mark.
"I don't accept that the sexual violence of a few men means that all fathers have to be treated as a potential threat. That is wrong and it will block positive change."
He said maternity services could be reformed "to engage the whole family and include fathers", and services developed "that facilitate mutual support between families".
"We know from research in the US that parents who share care increase family earnings," he added, saying Labour would be "helping family self help initiatives in the community and letting finance follow".