Similes and Metaphors - are similes a subset of metaphors?

The Wikipedia article on Metaphor agrees with your colleague:

Metaphor also denotes rhetorical figures of speech that achieve their effects via association, comparison or resemblance (e.g., antithesis, hyperbole, metonymy and simile, which are all types of metaphor).

(emphasis added)

The article cites "The Oxford Companion to the English Language (1992) pp.653–55" as a reference for the above information, but I don't have access to that publication to verify the statement directly.

Edit: Well, it turns out that I do have access to that reference. Here it is, from p. 653, paragraph 2:

METAPHOR ... (1) All figures of speech that achieve their effect through association, comparison, and resemblance. Figures like antithesis, hyperbole, metonymy, simile are all species of metaphor.