Suppose I have a response $Y$ and two features, $X$ and $Z$. Individually the features are not very predictive but their interaction is strongly predictive. Something like
$$Y = 0.5X + 0.5Z + 20XZ + \epsilon$$
Will just $X$ and $Z$ still have high mutual information with $Y$ because of the interaction term or will only the dependency of $Y$ on $X$ and $Z$ separately be captured?