Many couples dream about the day they will start their own family. Their minds are full of the family traditions they'll start, the fun trips they'll take and the great memories they will make together.

Kate and Peter Hill had this dream - a dream that was shattered one day in 2006.

Doctors said Kate would never conceive

In a video interview, the couple describes their incredible journey of not ever being able to conceive, to birthing miracle babies.

Kate was diagnosed with polycystic ovarian syndrome, a health condition that meant she might never be able to conceive. And to make matters worse, she wasn't ovulating.

But the Hills didn't give up. Kate took hormones to increase her chances of conceiving. And despite what doctors told her, she became pregnant with twins nine years later.

Unfortunately, she lost one of the babies due to a miscarriage early in the pregnancy, and the Hills were left with one baby.

Her pregnancy was rare

But Kate's miracle pregnancy wasn't even the most surprising part. Ten days after conceiving, Kate conceived again.

So Kate was once again pregnant with twins, but in a way that has only been documented ten times throughout all of recorded history.

Normally, twins are conceived when a woman releases two eggs or when one egg splits and becomes two cells. In Kate's situation, she released another egg after she was already pregnant.

The couple's obstetrician, Brad Armstrong, said he had never seen anything like this before. Superfetation, the name for getting pregnant while pregnant, was almost unheard of. It is so rare that he couldn't find any reviews about it on any medical review websites.

The way she conceived was an even bigger surprise

What makes this pregnancy even more rare is the fact that the couple had unprotected sex only once.

But once is all it takes. Sperm typically lives three to five days inside a woman's body, but that's not the case here. Because they conceived 10 days apart, that means the sperm lived twice as long as expected, making this miracle pregnancy even more of a miracle.

Now the Hills are a family of four

Kate gave birth to twin girls at the end of 2015, who she and her husband named Charlotte and Olivia.

Even though they are twins, the girls are different in many ways: weight, length, developmental stage and blood type. And today, their different personalities are coming through.

"Olivia is pretty loud, but Charlotte is the demanding one," Kate said. "They are definitely little miracles."