I’ve been looking for this for some time – the shares of 25 + year old persons, U.S. born and foreign born, by educational level. I found data here, then estimated the two populations for 25 or older. The results are inexact, but confirm that which we knew: a disproportionate share of adults with less than high school education are foreign born.
The table, however, does not reveal that in the past 10 or so years, recent immigrants are much more formally educated than earlier arriving immigrants. This shift reflects how the dominant type of immigrant 1980 – 2005 was from Latin American, since then from to Asia. The Asian immigrant population has almost doubled since 2000. The table shows that among all living persons 25 + years, 34% of U.S. born persons and 34% of foreign-born persons had a college or advanced degree. In 2013, 41% of recent immigrants had college or advanced degrees. Go here, here and here.