The group on Monday featured Winters and Vettori on its website in a video, telling the story of their marriage, Winters' firing, and Vettori's letter to the pope pleading for his intervention.
The couple, already planning on attending a full week of papal events in Washington and Philadelphia, were giddy with the news Monday night.
"Obviously we won't be talking to the pope, but we will be in the vicinity," Winters said of Wednesday's White House event. "But symbolically, it's a great step forward."
Winters and Vettori said the invitation left them feeling humbled and exhilarated.
"We continue to say it's the spirit at work," Winters said. "It's the people who have been supporting us, moving this issue forward and in front of people."
They continue to hope for an audience with Francis to discuss the lives and roles of the LGBT faithful in the church.
The Human Rights Campaign video featured Vettori reading the letter she wrote in July to the pope.
She choked up while asking Francis "to intervene on our behalf and countless other faithful Catholics so that we may not be condemned to live a life exiled from a church we so love and want to serve."
Winters, in the video, said, "We're asking the bishop to stop firing people for LGBT issues."
Archbishop Charles J. Chaput, through a spokesman, has repeatedly asserted that the Archdiocese of Philadelphia played no role in Winters' firing.
Waldron Mercy is sponsored by the Sisters of Mercy. By church law, the school is under the authority of the local bishop.
Chaput in July issued a statement praising school officials for their "character and common sense" in firing Winters.
Winters, hired by Waldron Mercy in 2007 as director of religious education, said she told the principal at that time that she was in a same-sex marriage.
That did not present a problem until this year, Winters said, when one parent complained to the school's board of directors and another complained directly to the archdiocese.
The White House did not respond to a request for confirmation and comment on the invitation.
Winters' firing drew national attention, with an outpouring of support and some anti-LGBT vitriol. The school hosted a series of private meetings with parents to discuss the controversy before the start of the new school year.
Parents of students attending Catholic schools in the archdiocese were required this month to sign a "memorandum of understanding" that on any question of religious principles and policies, "the final determination rests with the archbishop." A spokesman for the archdiocese said the memorandum had nothing to do with the controversy at Waldron Mercy.