One reason the US performs poorly on the infant mortality measure actually reflects differences in measurement between it and other countries--babies born very prematurely in the United States are recorded as live births, but in other countries might be reported as miscarriages. Because extremely premature babies have higher mortality rates, their inclusion in the US birth and mortality rate makes the US look relatively worse.
Nevertheless, when Chen, Oster and Williams control for reporting differences, and focus on microdata from the US, Austria and Finland, they find that the US continues to lag the others in terms of first year survival. What is particularly interesting is that the difference between the US and other countries accelerates over the course of the first year of life--as neonatal threats recede, the position of the US worsened relative to Austria and Finland.
Here is where inequality comes in--if when Chen and co-authors look at children born to advantaged individuals (meaning married, college-educated and white) in the US, they survive at the same rates as their counterparts in Austria and Finland. But the trio find that children of disadvantaged parents in the US have much lower survival rates than children of disadvantaged parents in the other countries. This may well be because Europe's safety nets make the disadvantaged less disadvantaged.
(Dylan Matthews blogs on this paper also).