Women enjoy only a "thin veneer" of equality in society, the new chair of the Equal Opportunities Commission (EOC) has said.
Time with the family is a major concern
Jenny Watson, appointed on Wednesday, said equality had "progressed" but only when "women live as men used to".
When women wanted to look after children or elderly relatives then inequalities kicked in, she added.
Meanwhile an EOC survey suggested that better support for families was becoming an important social issue.
The survey of 2,000 adults found that more people are concerned with spending time with their family than the standard of local health services.
Ms Watson said both men as well as women wanted to take a leading role looking after children.
"We need to harness this alliance to achieve a new era of true equality, one which sees family relationships and the care and nurturing that accompanies these as positive, and something deserving of public support," Ms Watson said.
"Far too many parents and carers still pay a poverty penalty as they try to balance work and family life."