Research carried out by the EHRC suggested that many families donπt have fixed ideas about men as the main breadwinners and women as carers, but that employment legislation has not kept pace with the shift in social attitudes.
The report, entitled Working Better, said: "Britain now stands out internationally for having a very long period of leave reserved for mothers, most of it at a low rate of pay, and for having a relatively weak parental leave.
"Together long, low-paid maternity leave and short, low-paid paternity leave convey the message that it is primarily women who are responsible for the care of young children."
Under the proposed plans, the first 26 weeks after the arrival of a new baby would remain dedicated to maternity leave for mothers but at better rates of pay, with the number of weeks paid at 90 per cent of pay increasing from six to 26 weeks. After six months, mothers would get the same 'parental leave' arrangements as fathers.
Fathers would still get two weeks of paternity leave at the birth of their child, but this would also rise to 90 per cent of their pay.
After the first six months of maternity leave, the report recommends that there should be three further sections of parental leave, to be taken at any time before the childπs fifth birthday. Each section of leave would be for four months, one taken by the mother, one taken by the father and one taken by either parent.
As a legal minimum, the first eight weeks of this parental leave would be paid at 90 per cent of pay. Parents, however, would not be allowed to go on leave at the same time.
The EHRC estimated that the changes would cost £5.3 billion, to be introduced in steps until 2020 when the new entitlements would be fully in place.
The report also proposed changes to the flexible working rules.
It said that although Britain appears on paper to have weaker flexible work legislation than other countries - a right to 'request' as opposed to a right to 'have' - in practice there is a wider range of alternative ways of working in the UK than elsewhere in Europe.
But the Commission also found that parentsπ awareness of the right to request is low and that there is a growing divide between workplaces where flexible working is 'business as usual' and workplaces where progress has been limited.
While ruling out any move to turn the right to request into the right to have, the report called for: the right to request flexible working to be extended to everyone, not just parents; a repeal of the 26-week employment eligibility criteria for requesting flexible hours; and the introduction of a formal right to request a return to full-time work after a previous change in working hours.
Nicola Brewer, chief executive of the EHRC, said: "Our report indicates some British employers are ahead of the legislation in terms of adopting modern ways of working and weπre heading in the right direction on flexibility.
"But when it comes to modern approaches to parental leave, we may need to try a different route. We are proposing one of the most radical changes in our approach to parental leave in a decade. We have spoken to parents, to employers, to unions and to leading academic experts in the field, and we believe that the Working Better report lays out a road-map to 2020 which will put Britain ahead of the curve in terms of modern working practices."
However, the CBI questioned the cost of the plans.
Katja Hall, the CBI's director of HR policy, said: "Given the alarming state of the public finances, these plans, which would cost taxpayers an extra £5.3 billion, are unaffordable. It makes far more sense to focus on encouraging flexible working, which is open to both parents but does not materially increase costs for business and the taxpayer.
"While this report raises some interesting talking points, the proposal to introduce paid parental leave to be shared between parents would be complex and costly for companies to administer."