With his voice occasionally breaking with emotion, Mr Biden recounted the phone call in December 1972, telling the 29-year-old senator that his wife Neilia and one-year-old daughter had been killed in a car crash while Christmas shopping.
"And just like you guys know by the tone of the phone call, you just knew," he said. "You just felt it in your bones: Something bad happened."
As he left the US Capitol building to identify the bodies and tend to his two young sons, who were critically injured in hospital, he recalled looking up at the building's cavernous rotunda.
"I remember looking up and saying, ‘God,’ as if I was talking to God myself, ‘You can’t be good, how can you be good?"
"I probably shouldn’t say this with the press here, but it’s more important, you’re more important. For the first time in my life, I understood how someone could consciously decide to commit suicide," he told families at a grief seminar in Virginia.
"Not because they were deranged, not because they were nuts, because they had been to the top of the mountain, and they just knew in their heart they would never get there again."
Standing in front of pictures of soldiers killed in action, he promised "it can and will get better".
"There will come a day," he said "when the thought of your son or daughter, or your husband or wife, brings a smile to your lips before it brings a tear to your eye."
Speaking of meeting his second wife, Dr Jill Biden, in 1977, he said he felt "guilty as hell" but urged widows and widowers to seek new happiness after their loss.