I think it might be "normal" for parents of a kid to be in denial at first especially if there are no warning signs.
But it's totally NOT normal for a parent to spend pretty much the entire life of said kid in denial over everything having to do with the kid. Cindy seems to have spent months & in some cases, years, in denial as far as Casey being pregnant, Casey working, Caylee having a babysitter, etc. She was the golden child in that house even if she was a lazy brat. Sounds like the oldest Tsarnaev brother was also his mom's golden child...maybe younger bro went along with older bro because he grew up learning from his mom to do so (this is NO WAY excuses his actions).
I think we've seen examples of parents who have told police in interviews, at least, something along the lines of "I can't believe/don't want to believe..." but also seemed to spill all about things their child was doing that were weird, freaked them out, or down right scared them. Jodi Arias's parents, in police tapes, came off that way to me. George seemed, in some of the videos with LE, to also spill all about Casey and seemed to accept the fact that she had killed Caylee. In one, he even asked LE that if they thought Casey killed Caylee, to let him know because it would kill his wife and he wanted to prepare her/help her (or something similar). I think George thought for a long time he could get Cindy to come around to accepting Casey killed Caylee, but in the process, Cindy (the dominant personality in that relationship) actually brought George around more to her side (again, not excusing George for not washing his hands of the whole lot of them).
Denying at first one shocking thing your kid did may be normal.
But denying everything they've done wrong their whole lives isn't normal, no matter how prevalent it may be among criminals' parents. That's not denial, that's enabling.