Zompist Bboard Again

Are there any languages that have both an antipassive and a passive voice and how does it work? I am really thinking of ergative languages, because in each of these voices there would only be one argument - in the absolutive case - so presumably they would have to be morphologically distinct in some way - and from the active voice as well?

Yes, that happens. WALS has 12 listed (as opposed to 19 that have antipassives without passives), you look here; presumably those aren't all errors. I'd expect the active/passive/antipassive distinction to be made overt somehow, otherwise I doubt they'd be counted as distinct voice.

(There are cases like English "cook," which can be used either transitively or intransitively, and whose subject as an intransitive verb can correspond to either its subject or object as a transitive verb---"I cooked the stew", "I cooked", "The stew cooked." But that last example doesn't really have the semantics of a passive, it's more an anticausative.)

Two of that dozen of languages on WALS are Jakaltek and Tzutujil, both Mayan languages. It is true that most or all Mayan languages have distinct verbal constructions usually labelled "(medio)passive" and "antipassive" (sometimes there's a "completive (medio)passive" too). I'm not familiar with these languages at all, but you can probably consult the grammar of any Mayan language for this kind of thing.

Basque and Chamorro are also listed. Basque resources may be easy to consult. I'm quite surprised by Chamorro because unlike Mayan languages and Basque, it's not a language with prominent ergativity as far as I know (but maybe I'm wrong about that regarding Chamorro).

Antipassives aren't limited to languages with ergative morphosyntax, though. (They might be more obvious given that the subject's case will likely change in an antipassive.) The WALS chapter lists 17 languages, one of them Chamorro, as having antipassives without ergative morphology.