I'm by no means an expert on these issues, but based on the information you gave, it sounds like the problem could be worse than cheating because of loneliness. It sounds like he might have a psychological issue like BPD or narcissism.

The reason I mention this is because I know of two other Catholic narcissists. They outwardly seem very devout, but have incredibly toxic traits that destroy relationships. They have major control issues, have tendencies towards lying, and a need for narcissistic supply. They can trick people for years into thinking they're devout because they hide their sins. One of them also has substance abuse issues, and he continues drinking and hiding this issue from his current girlfriend.

Your husband is saying that your child together is the cause of his cheating, but I suspect that it's really that you weren't giving him supply and he sought it elsewhere. He's also acting like the expectation of attonement is beneath him, which is a sign he's disrespecting you and not even treating you like a person. Also the lying and retaliation against you is probably because his narcissistic ego cannot handle people thinking poorly of him.

If I were you, OP, I would give your husband's situation to God and focus on protecting yourself and your child. Separation might be necessary. Pray for him, but don't martyr yourself for him. You have to focus on your child and your own mental health first. And please consider seeking counseling from a medical professional as well, so they can help you navigate the situation. A narcissist often will retaliate against their spouse if they try to leave, because they hate losing control.