They found that
“Although both white and Latino adolescents from two-biological-parent families are less likely to use drugs than their counterparts from differently structured families, Black youths who come from similar two-parent families are among the most likely users of both alcohol and marijuana.”
Amey and Albrecht don't have a good explanation for this, and neither do I. My best guess is that the black two-parent families have fewer married parents than the white and Latino two-parent families. The black marriage rate is so low that it is common in studies like this to conflate married and cohabiting black parents. Cohabitors, especially cohabiting fathers, are less likely to discipline kids strictly than married fathers are.