I would love to see the study you are referring to, because I've just done an analysis of inflation-adjusted growth in household incomes, particularly among families raising kids, and saw no such evidence from 1976 to 2004. Indeed, the average did go up, but the average is driven by most of those gains being concentrated in the top 10% of families raising children; the distribution is such that the bottom half of the distribution of families raising children stagnated or fell, and that's after taxes.
On May 29th, 2007. See this statement in context.