So Father's Day in their Rozelle home in Sydney traditionally begins with eggs on toast in bed, followed by a banana split created by their youngest son, Val, 6.

Given both men deserve a break on this annual day for spoiling dads, the biggest question is: "Who is going to get out of bed and go and get coffee?", Mr Duffy says.

The rest of the day is spent having lunch out and going for a walk or a bike ride together, before meeting up with extended family in the afternoon. This year, Val has also made something special at school involving a crocodile.

Corey says the day is important to show his dads "how great they are". "They've done a lot for you and you should give back."

Mr Duffy adds: "It's just a reminder for us to stop and celebrate our family."

This year, Father's Day is being celebrated in the shadow of the same-sex marriage postal vote, with voting forms due to be mailed out to people from September 12.

According to the 2016 Census, there were 46,800 same-sex couples in Australia. Of those, about 6800 had children.

Mr Duffy, Taronga Zoo's director of conservation and science, and Mr Murphy, the director of digital strategy at Westpac, were married in New Zealand last year but want the right to be married in Australia.

"As a couple, it's really important. We love each other," says Mr Duffy.

"It also adds to what we want to build as a family, which is safety, security and love."

Both men say it is impossible to explain to their sons why they can't get married in Australia. They are also worried about Corey and Val being exposed to hurtful language during the postal vote campaign, where "no" campaigners like former prime minister Tony Abbott are arguing against same-sex marriage because it is "better for kids" to have a mum and a dad.

As the two dads point out, children have nothing to do with the issue of same-sex marriage.

"It's about equal rights and respecting everyone," says Mr Duffy of the upcoming vote, adding "we've had our children for over a decade."

The Australian Medical Association and Australian Psychological Association recently told Fairfax Media there is no scientific evidence that children of gay and lesbian parents had poorer outcomes than those of heterosexual parents. Marriage equality campaigner Tiernan Brady has also described the "no" campaign's focus on children as a "red herring".