Immigrants and mobilityby
Here's a little chart showing that at least some immigrants are still upwardly mobile.
In 1995, families headed by immigrants who entered the country in the 1980s had a 26.6% poverty rate. That plunged to 14% in 2001, before bouncing back up to 16.4% in 2003.
Now, I don't know about you, but a 40% decline in the poverty rate (26.6% to 16.4%) sounds like pretty good upward mobility to me.
Added: Data comes from the Census Bureau