“But we are already a family in our minds and hearts,” Michael said.

The mundane truths — and challenges — of gay couples who parent have been hard to find in the heat of the national debate. Gay parents describe the difficulties of completing even small administrative tasks. At the hospital, the Duggan-Tierneys might be greeted with, “Are you the dads?” But a government official renewing Reid’s passport expected to meet the boy’s mother, the men said.

Earlier this week, a Fairfax/Ipsos poll found that around 70 percent of Australians would vote in favor of same-sex marriage in the government’s survey.

The vocal “no” camp is undeterred by the recent opinion polls.

Opponents of gay marriage argue that children would “lose the right” to have a mother and a father and that legalizing marriage would open the door to “radical gay sex education programs.” They view themselves as David staring down a politically correct Goliath, and with the postal vote results expected in November, they are predicting victory.

“We have many hundreds of thousands of concerned people who will, like ‘Brexit’ and like Trump, move and assert their quiet preference over the coming weeks,” said David van Gend, a spokesman for the Coalition for Marriage, a group that opposes legalization.

Supporters of same-sex marriage say the concerns about children are misguided. They point to a recent Columbia Law School report that analyzed 79 studies on the well-being of children with gay or lesbian parents. The researchers found that 94 percent of those studies concluded that children of same-sex couples fared no worse than those raised by heterosexual parents.

Dr. van Gend said Columbia was engaging “in public advocacy” and “mischievous science” in releasing the summary, and he said that none of the studies that showed positive outcomes had significant data.

Image “There are hurtful things being said,” Senator Penny Wong, a member of the Labor Party and a gay parent, said about the campaign against same-sex marriage. Credit... Mandel Ngan/Agence France-Presse — Getty Images

Simon Crouch, an Australian researcher whose study was cited by Columbia, said the report is solid and reliable. “Three decades of research in this area points to no difference — and sometimes, some benefits — for children in same-sex parent families,” he said.