The Economist has an interesting article on what goes on in a bilingual child's mind. The researchers found that:
some aspects of the cognitive development of infants raised in a bilingual household must be undergoing acceleration in order to manage which of the two languages they are dealing with.
The caveat in the research is that the findings relate to children who grow up in homes where two languages are commonly spoken, rather than in situations where one language is spoken at home and another at school.