Mr Miliband said he and Louise, a professional violinist, went through "emotionally exhausting" years of IVF treatment before deciding to adopt sons Isaac, now five, and Jacob, two.
The Milibands chose to adopt in Louise's US homeland, where it is easier for would-be parents to find newborn babies.
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Hide AdBut Mr Miliband denied it was a "baby supermarket" arrangement.
"I hate the baby supermarket thing – it was the opposite. Birth parents can change their mind up to the last minute," he said.
"Going to America to meet our babies was in a way like giving birth. It was incredibly exciting, but nerve-racking."