Hans-Peter Blossfeld & Andreas Timm edited an interesting volume a few years ago, Who Marries Whom? Educational Systems as Marriage Markets in Modern Societies. Educational homogamy measures what proportion of married people have spouses with the same level of education that they do.
The main finding is that homogamy rates have increased significantly over the 20th century. Women are more educated than they used to be. This evens out the pool at each educational level, makes it less likely that women would marry up (what Blossfeld calls the traditional pattern) and more likely that women would marry down. And the inverse for men.
For the 40-something cohort in the United States, about 27% of the women married up, 21% married down, and 51% married someone with the same school degree.
In the U.S., women have been more equal to men in primary and secondary education, and high school education is predominant, way ahead of Europe. Homogamy rates are lower than in Europe, but still much higher than the predicted value. This seems to be because women are spread across more educational credentials, so the odds of them marrying within any one of them is lower.