Philosoraptor called my attention to the following chapter in the System of Logic:
A System of Logic, Ratiocinative and Inductive Being a Connected View of the Principles of Evidence and the Methods of Scientific Investigation By John Stuart Mill
So, in effect, utility is the theory of all practical reason, the departments of which are ethics, politics, and aesthetics (where the last is understood as encompassing all matters of good and bad taste). What I find particularly interesting is that Mill uses this as an argument against intuitionists:
A System of Logic, Ratiocinative and Inductive Being a Connected View of the Principles of Evidence and the Methods of Scientific Investigation By John Stuart Mill
This is a fascinating (although I think somewhat implausible) argument. There is nothing about intuitionism as such that requires that it apply only to moral judgments, and certainly Whewell's intuitionism, which is the major contemporary rival to Mill's utilitarianism, does not. But it is notable that Mill here uses a failure to allow for a non-moral aspect to human life against the intuitionists -- which is a criticism he had also made, in slightly different form, against Benthamite utilitarians.