Anxiety and depression share genetic influences, and have been associated with similar cognitive biases. Psychological theories of anxiety and depression highlight threat interpretations of ambiguity. Little is known about whether genes influence cognitive style, or its links to symptoms. We assessed ambiguous word and scenario interpretations, anxiety and depression symptoms in 300 8-year-old twin pairs. There were significant correlations between both negative interpretations of ambiguous words and scenarios and depression symptoms after controlling for anxiety symptoms (r = 0.13 and 0.31, respectively), but no significant correlations with anxiety independent of depression. Genetic effects ranged from 16% for depression to 30% for ambiguous word interpretations. Non-shared environmental influences were large (68-70%). Both genetic and environmental influences contributed to the association between depression and ambiguous scenario interpretations. These findings support psychological theories, which emphasise the role of environmental stress both on the development of threat interpretations and on their links with symptoms. The data also support a role for genetic influence on threat interpretations, which may mediate responses to stress.