Model Laura Lacole is due to marry footballer Eunan O'Kane, who plays for Leeds United and the Republic of Ireland, in Northern Ireland in June.
Humanist weddings are not recognised by law in Northern Ireland, so couples must also have a civil ceremony.
Northern Ireland's Attorney General is expected to intervene in the case.
The couple attended a judicial review hearing at Belfast High Court on Friday to challenge the current legislation.
Opening the case, their lawyer claimed the pair were being denied rights afforded to religious couples.
He said all they were asking for was the same protection afforded to those of different belief systems.
Ms Lacole, from Belfast, and Mr O'Kane, from County Londonderry, have both described themselves as humanists - a non-religious combination of attitudes, ethics and beliefs centred on human experience and welfare.
Humanists adhere to a scientific view of the world and believe humans steer their own destiny.
Ms Lacole, 27, is also vice-chair of Atheist NI.
"Religious people, from pagans to Free Presbyterians and everything in between, enjoy a substantial legal privilege under law," their lawyer said.
He argued that the State "gives its legal blessing to such marriages" but "denies the same privilege to equally valid groups".
Their lawyer added that, as the law stood in Northern Ireland, the couple's wedding on 22 June would be "legally meaningless".
Humanist wedding ceremonies are legally recognised in Scotland and the Republic of Ireland but not in England, Wales or Northern Ireland.
The couple are taking the judicial review against the General Register Office for Northern Ireland and Stormont's Department of Finance.
Their lawyer told the court the case was of "huge public interest".
He pointed out that were 4,290 humanist weddings in Scotland in 2015 - more than those conducted by the Church of Scotland.
Northern Ireland's Attorney General, John Larkin QC, has applied to participate in the landmark legal challenge and could make submissions on Friday.
A couple who want their humanist marriage ceremony to be legally recognised are being discriminated against, a court has been told.