Such are statistics. What almost tripled was the absolute number of unmarried cohabiting couples with children under it. What went down from 68% to 64% was the proportion of US children under 18 who lived with their two parents who were married and living together. Unchanged: children living with only the mother (24%), only the father (4%), or neither parent (4%).
Why are there such dramatically different ways of telling the same story? First, a smaller proportion is subject to change a lot more radically, relative to its former size, than a larger proportion is. When the number of states with a black senator doubled from 1 to 2, the proportion of states without one only went down by 2%. Also, the first number used absolute numbers, which could also go up as population, and particularly the child population, increases.
Another big caveat: This study, like most statistics, substantially undercounts family disruption because it does not distinguish between the child's two actual parents, still married and/or still cohabiting, and one actual parent who's married to someone else who's referred to as a stepparent. "For this indicator, unless otherwise specified, a two-parent family refers to parents who are married to each other and living in the same household. They may be biological, adoptive, or stepparents. The Current Population Survey identifies all parents who are family or subfamily heads. Where cohabitants are concerned, until 2007, the CPS did not ask whether that person was also the parent of the child." Also, people are more likely to call themselves stepparents if they are married, not just cohabiting, so that is yet another distorting factor which increases the measurement of married parents versus cohabiting ones.
Ironically, the report's introductory section, titled "Importance", emphasizes how important the differences are between children living in truly intact married families and those who experience divorce or unwed birth and then live with stepparents. But in most cases, the government simply does not collect the data on that extremely important distinction, adding that insult to all the injuries done to marriage, families and children over the decades.
With that in mind, here are some excerpts. The article also has many useful links to many current sources of family statistics, the full study, and the underlying data.
The proportion of children living with both parents, following a marked decline between 1970 and 1990, has fallen more slowly over the most recent two decades, dropping from 69 percent in 2000 to 64 percent in 2014. ...
Between 1960 and 1996, the proportion of all children under age 18 who were living with two married parents decreased steadily, from 85 to 68 percent. This share was stable during much of the late 1990s and into the 2000s, but by 2012 it had decreased to 64 percent. The rate was stable between 2012 and 2014.
In 1960, the proportion of children living in mother-only families was eight percent, but by 1996 that proportion had tripled, to 24 percent. Since then, it has fluctuated between 22 and 24 percent, and was at 24 percent in 2014. Between 1990 and 2013, the share of children living in father-only families has fluctuated between three and five percent, and was at four percent in 2014. The proportion living without either parent (with either relatives or with non-relatives) has remained steady, at approximately four percent.
In 2014, there were 3.1 million cohabiting couples (unmarried) with children under 18. This number has been steadily increasing: in 1996, it was 1.2 million. ... Compared with married couples with children, cohabiting couples with children tend to be younger, less educated, lower–income, and with less secure employment. ... In eight percent of unmarried couples with children, neither person was employed in 2014, compared with only four percent among married couples with children.
In 2014, 34 percent of black children were living with two parents, compared with 85 percent of Asian children, 75 percent of white children, and 58 percent of Hispanic children.
[The following are from the introductory section, titled "Importance"]
Both mothers and fathers play important roles in the growth and development of children. The number and the type of parents (e.g., biological, step) in the household, as well as the relationship between the parents, are strongly linked to a child’s well-being.  Among young children, for example, those living with no biological parents, or in single-parent households, are less likely than children with two biological parents to exhibit behavioral self-control, and more likely to be exposed to high levels of aggravated parenting, than are children living with two biological parents. Children living with two married adults (biological or adoptive parents) have, in general, better health, greater access to health care, and fewer emotional or behavioral problems than children living in other types of families.
Among children in two-parent families, those living with both biological parents in a low-conflict marriage tend to do better on a host of outcomes than those living in step-parent families. Outcomes for children in step-parent families are in many cases similar to those for children growing up in single-parent families., Children whose parents are divorced also have lower academic performance, social achievement, and psychological adjustment than children with married parents.
Single-parent families tend to have much lower incomes than do two-parent families, while cohabiting families fall in-between. Research indicates, however, that the income differential only partially accounts for the negative effects on many areas of child and youth well-being (including health, educational attainment and assessments, behavior problems, and psychological well-being) associated with living outside of a married, two-parent family.,