Identified only as Imogen, she rang into the LBC radio station to ask the Labour leader if he would stop mothers and fathers who care for their children at home being "penalised in the tax system".
When he told her he had no "easy solution" to the issue, she replied: "I don't think you have any solution, Mr Miliband."
But Mr Miliband insisted that he could not pledge unfunded tax cuts.
"Where's the money going to come from?" he asked, saying that if elected in 2015 his government would face an "incredibly difficult" set of financial circumstances.
Campaigners and some Conservative MPs have criticised the Tory-Lib Dem coalition over its treatment of stay-at-home parents.
They want transferable tax allowances to help couples look after their own children.
Figures suggest that families with stay-at-home parents can face a higher tax burden than others.
Mr Miliband also faced questioning from another listener who asked him if "knifing" his brother David in the Labour leadership contest showed he had the required toughness to be Prime Minister. Mr Miliband admitted that going head to head against his sibling had been difficult, but described their relationship now as a "lot better".
He also revealed that when he had first told his brother that he planned to stand against him, David had said "may the best person win".
But he added that taking on his brother David in the Labour leadership election was the "toughest thing" he had ever done.
"It was really tough taking on my brother, it's the toughest thing I have done," he said.
"And the reason I did was because I thought I had something distinctive to say about how Labour needed to change and move on from New Labour, and how the country needed to change, and I thought I was the best person for the job and best capable of doing that. And it was painful and it was really hard."
Mr Miliband said he had shown toughness in his leadership of the Labour party so far.
"What I am proud of having done as leader is taking some really hard decisions when it has been tough. I have had tough opponents, like the energy companies, like the banks."