Good points so far. This question is not going to get you any meaningful information because every family is different no matter what their race or ethnicity or religion, and trying to answer this probably just leads to an impression of stereotyping. Some African-American families do just fine in every way, and some struggle in lots of ways. The same is true of Caucasian families. One area of difference, which is probably hard to document and which I'm only guessing is true, is the expectations each has of achieving something significant in their lives. It does seem as if the average Black family views its opportunities for achieving success as being more limited than the average White family might.
My view on this is that they are not fundamentally different in any way. This is true of families all over the world. The family unit dates back millenia, and precedes today's natons and societies. African-American families love their children, want them to be safe, want to provide for them and give them a better future than they had, just like everyone else.
I would caution anyone from posing questions that tend to lock people in racially or ethnically stratified roles. I think it's dangerous on many levels and probably goes far in denying the essence of who individuals are and how they act. This is the first point to be made. At the same time, I do believe that one could examine how different families' embrace of religious expression could be seen as different. The experience of church and service at a predominantly African- American church can be seen as different than that of a predominantly White church. The President's memoir, "Dreams from My Father," can help to bring this to light when he describes his first service at Trinity United Church in Chicago. The expression of spiritual fervor is in a different form in both settings. Families' embrace of this religious reality is different based off of this. In no way does this attempt to paint with one brush how African- American and Caucasian families' view religion, but rather seeks to bring to light a potential difference in each family's view of religion through examining the religious experience of each group.
I can think of two ways in which the average African American family is different from the average white family. I put the word "average" in bold because you must not assume that all black families or all white families actually do follow these patterns.
The first difference is that African American families are much more likely to be headed by a single mother. African Americans are more likely to have children outside of marriage.
The second difference is that African American families are more likely to have lower incomes.
Please note that I am simply stating that these things are true and am not saying anything about what causes these conditions.