Unbelieving parents do not have a covenant with God and are in his disfavor. Their children would not be under a "spiritual blanket" and would face the same punishment as their parents.

I think this idea is supported by the cleansing of Canaan. Joshua was commanded to kill every living thing, which included children and babies. Infants were considered unclean since they were members of a pagan culture that their parents participated. Israeli children were considered clean because they were part of God's chosen culture.