Abigail and Micaela Bachinskiy are now thriving in recovery, as their parents Liliya and Anatoliy Bachinskiy get accustomed to the girls being separated

The parents of Abigail and Micaela Bachinskiy, the twin girls who were born conjoined at their heads, are speaking out after their daughters' "one-in-a-million" separation surgery.

Liliya and Anatoliy Bachinskiy say they're overjoyed following their 10-month-old daughters' successful 24-hour surgery at UC Davis Children’s Hospital on Oct. 23 and 24, but they're still getting accustomed to no longer seeing the baby girls attached at their heads.

"It took me a minute to hold them because they were so unique," Anatoliy recalls to PEOPLE (the TV Show!). "You got used to them being together, and now you're seeing two different girls, two different bodies and ... it's just amazing."

"It was very special," adds Liliya. "I was crying when I held them, tears were filling my eyes. When you hold them, if you have some worries [internally]... they just run away. I wasn't heavy inside, I was so relieved."

That relief had been a long time coming for the California couple, who learned that Abigail and Micaela were connected at the head, with an extremely rare condition known as craniopagus twins, back when Liliya was 11-weeks pregnant in 2019.

"I was shocked and I couldn't believe it," says Liliya, adding that she first thought it was a "misunderstanding" and later began to worry. "But later on, God just gave me peace inside, and I just stuck with that. And my husband was supporting and encouraging me."

The Bachinskiy family
| Credit: Luliana Photography

Despite their rare condition, Liliya and Anatoliy — whose dad is a twin — say they were thrilled to be welcoming two girls, as they were already parents to three boys, who are ages 9, 7 and 6.

"I cannot express how excited I was. I almost jumped on the doctor," jokes Liliya. "I always wanted twins, even before I got married. I thought that would be cool to have, but I'm like, 'Ah, it's not going to happen so I'm not going to [spend] too much [time] dreaming about it."

And while expecting twins was quite special, the couple soon learned that their daughters would become some of the most special ones in the world as they prepared to undergo the "landmark" surgery.

"The condition they have, it's very unique," explains Anatoliy, who notes that Mika was initially given a lesser chance for survival because she was the smaller twin. "With our doctor, he told us everything should be fine, but there's always that chance that anything can go wrong."

"The doctors were always saying one in a million," says Liliya. "But I had a feeling because I saw God hand through the pregnancy, so many miracles, like big miracles, you know? And I just knew that God's taking care of this."

Liliya Bachinskiy with her kids
| Credit: Luliana Photography

On the day of the surgery, Anatoliy stayed home with their three boys, while Liliya remained at the hospital with family members.

Over the course of the next 24-hours, Liliya kept their loved ones in the loop as she prayed for a smooth procedure, which was led by a group of more than 30 surgeons, nurses, anesthesiologists and other key surgical staff, who had prepared for this for months.

By 6 a.m. on Saturday, doctors confirmed the surgery was complete and the girls made it through without any complications.

"Dr. [Granger] Wong, said to me, 'Liliya, can you imagine how many things could've happened? Through preparation, through the surgery, after surgery. And none of them happened,'" recalls the mom of five. "And I'm, like, 'That's amazing.'"

"A lot of people were supporting us and everybody wanted to know, so it was just good to know that everything went [well]," adds Anatoliy. "They're miracle twins."

The Bachinskiy kids
| Credit: Luliana Photography

As the girls continue to thrive in their recovery, their parents say they've enjoyed watching their different personalities shine through — and seeing the unbreakable bond they already share.

"From day number one, you could tell their personality [and] who is the boss," explains Liliya. "Abi, she's bigger and she's more bossy. But Mika, she is more gentle... I think they will get along very well because they're different and will complete each other."

"They love each other and you can tell, even when being separated right now. The first couple of days, Mika would reach her hand to find Abi and Abi was looking for Mika. That was so cute," she continues, with Anatoliy chiming in, "They would always hold hands when they sleep."

Liliya Miroshnik and Anatoliy Bachinskiy with their three sons
| Credit: Luliana Photography

The Bachinskiys also want to express their gratitude to the hospital staff at UC Davis Children's in Sacramento, who made this new chance at life for their twin girls possible.

"We're really, really thankful," Anatoliy shares. "They have a really amazing crew here, so, that's what makes the whole journey even easier."

"To say that we are grateful, it's nothing," adds Liliya. "They're like family to us right now. After all we went through together... we just love them for what they've done and we  want them to know that we will be so grateful for the rest of our life."

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