The preference for partners of the same education has significantly increased for white individuals

See New results on assortative mating by education Tyler Cowen. It seems like well educated whites want partners that will share their values in developing the human capital of their children (like sending them to college). So you get more households with two high income earners and they try very hard to make sure their kids grow up to be well educated and marry someone else well educated (that they might meet in college).

"Partner Choice, Investment in Children, and the Marital College Premium, by Pierre-André Chiappori, Bernard Salanié and Yoram Weiss

We construct a model of household decision-making in which agents consume a private and a public good, interpreted as children’s welfare. Children’s utility depends on their human capital, which depends on the time their parents spend with them and on the parents’ human capital. We first show that as returns to human capital increase, couples at the top of the income distribution should spend more time with their children. This in turn should reinforce assortative matching, in a sense that we precisely define. We then embed the model into a transferable utility matching framework with random preferences, a la Choo and Siow (2006), which we estimate using US marriage data for individuals born between 1943 and 1972. We find that the preference for partners of the same education has significantly increased for white individuals, particularly for the highly educated. We find no evidence of such an increase for black individuals. Moreover, in line with theoretical predictions, we find that the “marital college-plus premium” has increased for women but not for men."

See also On Assortative Mating from Greg Mankiw.As mentioned above, we are getting these very high income households. When the government measures how equal or unequal the distribution of income is, it is often by household. So this process is increasing the difference in incomes between the poorest and richest households. The gini coefficient mentioned below goes from 0 to 1 and higher means less equal.

"A new working paper concludes:

"Data from the United States Census Bureau suggests there has been a rise in assortative mating....[I]f matching in 2005 between husbands and wives had been random, instead of the pattern observed in the data, then the Gini coefficient would have fallen from the observed 0.43 to 0.34, so that income inequality would be smaller""

See also Higher Education Attainment by Family Income: Current Data Show Persistent Gaps by the Association of American Colleges & Universities. Excerpt:

"Among students in the bottom socioeconomic quartile, 15 percent had earned a bachelor’s degree within eight years of their expected high school graduation, compared with 22 percent in the second quartile, 37 percent in the third quartile, and 60 percent in the top quartile."

So if you are at the bottom, you are much less likely to get a college degree than people at the top. If you were born into the top quartile, you are 4 times more likely to get a degree than someone from the bottom.

The table below (from Mark Perry) shows that the top quintile has 2 income earners while the bottom has 0.42. 78.1% of the top quintile are married households. For the bottom it is 16.9%.  62.2% of the people 25 or older in the top quintile have bachelor's degrees but it is only 13.7% for the bottom. So the top quintile tends to be married couples where both spouses work and have college degrees.