The Registration of Marriage Bill, led by the Dr Alan Smith, Bishop of St Albans, has proceeded to the House of Commons to be considered by MPs.
Bishop Alan said he hopes the House of Commons will correct "a clear and historic injustice".
"As someone who has performed hundreds of marriages, it has always seemed shocking to me that mothers are systematically overlooked.
"This injustice dates to 1837 when children were viewed as a father's property and little consideration was given to women. In this centenary year of women's suffrage, it is time to make this long overdue change.
"I am pleased to have had the backing not only of Peers and many in the Church, but a huge number of others, including tens of thousands who have signed public petitions, campaigners for women's equality, and even genealogists."
The bill would also introduce electronic marriage registers.
According to the Church of England, this is the first time a Bishop's Private Member's Bill has proceeded to the House of Commons in more than 20 years.
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