"This wasn't something they ever imagined was possible," says the source. "They so strictly limit their exposure to these sorts of outside influences – from websites to even the sort of television they watch, if they turn on the TV at all – that they were absolutely baffled by how this could have been possible."
Amid reports Josh had signed up for Ashley Madison, a website that specializes in facilitating extramarital affairs, Jim Bob, Michelle and Josh broke their silence with a statement on the Duggar family website Thursday.
In a statement that was later amended, 27-year-old Josh wrote that he has been "the biggest hypocrite ever" and confessed to a secret porn addiction, as well as being unfaithful to his wife.
In their statement, Jim Bob, 50, and Michelle, 48, said that when they learned of this late last night their "hearts were broken," and ask for prayers for Josh, Anna, their grandchildren and their entire family.
RELATED VIDEO: Josh Duggar Admits to Being 'Unfaithful' to His Wife
According to the source, the heads of the 19 Kids and Counting household are "feeling more devout than ever because they are turning 100 percent to God and prayer and their church community to help them through this."
Adds the source, "Their faith is in no way rocked by this."
The source adds that Jim Bob and Michelle are "devastated" at the news of the recent scandal – which comes just three months after a first scandal surrounding Josh broke in mid-May, revealing Josh had been accused of molesting five underage girls as a teenager, including two of his sisters, Jessa (Duggar) Seewald and Jill (Duggar) Dillard.
"They just don't know who this person is who could have done this," says the source of Josh's admission on Thursday. "It's like he's a completely different person from who they thought he was, and they're still trying to reconcile all that they know is good about Josh, whom they will always love and adore, with what they've learned now."
RELATED VIDEO: Jim Bob and Michelle Duggar 'Stunned' by Son Josh's Cheating, Pornography Scandal
"As for Josh, in this moment, I would assume he feels like his life is ruined," says the source. "Don't forget that the main aspect he focused on in his attempt to fix things after the molestation scandal was the fact that he was young when that happened and that he had since rebuilt himself, turned to a righteous path and was a good, upstanding, decent man who had learned from his mistakes."
"The whole idea was that people should forgive what he did when he was a teenager because he was such a great guy now," continues the source. "So for this to come to light …. He's ruined. It will be such a steep and practically impossible climb to come back from this."
Josh has four children with wife Anna, 27, and a source with ties to the family told PEOPLE she will likely not be leaving him in the wake of the new scandal: "Divorce is not even something that will be discussed."
"In the end, Josh and Anna will pull through this, Jim Bob and Michelle will weather this and they will give a lot of praise and glory to God for helping to strengthen their bonds to each other and to Him," says the source. "This will be seen as a test, and they – all four of them – will be determined not to fail."
For much more on the Duggars, subscribe now or pick up this week's issue of PEOPLE, on newsstands Friday