Darren Burnside has lodged a petition with the Scottish Parliament, calling for the removal of the "outdated law" which allows the Church to approve or disapprove teachers "in regard to their religious belief and character".
He claims his partner, a primary teacher seeking work in the city, is being discriminated against because she is not a Catholic. She cannot find a permanent job in Dundee, yet there are vacancies in Catholic schools, he says. On three occasions, she has taken up temporary contracts in Catholic schools but has been unable to secure a post.
"In this time of credit crunch, we need to have permanent jobs, and to be discriminated against because she isn't a Catholic is a disgrace," Mr Burnside says. "She is happy to do any religious practices the church requires, and does so when she teaches there temporarily. If this was the other way round and a Catholic was not allowed a job because they were applying for a Protestant school, there would be an outcry."
The Education (Scotland) Act 1980 entitles the church or denominational body to approve the religious belief and character of prospective teachers.
The entitlement was challenged at an employment tribunal in 2006 by David McNab, a self-confessed atheist. He accused the church of discrimination on the grounds of his religious beliefs by preventing him from applying for a promoted post teaching pastoral care in a Glasgow school.
Although Mr McNab won, the tribunal reaffirmed the Church's right to approve all teachers in its schools under the Act.
Michael McGrath, a director of the Scottish Catholic Education Service, commented: "This is about ensuring people who teach in Catholic schools are qualified to do that and to do the job they are employed to do. That includes the teaching of religious education."
The Parliament's public petitions committee plans to take the petition forward by seeking views from the Association of Directors of Education in Scotland, the Scottish Catholic Education Service and the Educational Institute of Scotland.
It will also write to the Scottish Government to find out if plans to amend the 1980 Act or revise the guidance given to local authorities.
SNP MSP John Wilson, who sits on the committee, said: "There is certainly an issue to examine in how we marry anti-discrimination law with what has been a tradition in the employment of teachers in education authorities."