Is it logical - and grammatical - to say "that husband of yours"?

"That husband of yours" and "that wife of yours" are grammatical and idiomatic. Whether or not they are "logical" is a matter of opinion. I don't think they're particularly illogical, as I explain below.

I can see why you would ask this, since various people have said that double genitives such as "of mine" or "of yours" suggest the existence of multiple things:

• "X of mine" is mostly used when you want to indicate that something is one of many that you own or are associated with. If, say, you have many cars, you might point to one and say, "That is a car of mine." But if you only have one, you normally say, "That is my car." (If you have many, you could also say, "That is one of my cars.")

  That is, it's almost always "an X of mine", not "the X of mine". I don't think I've ever heard someone say, "That is the car of mine" or "She is the mother of mine"; it's always "That is my car", "She is my mother", etc. "The X of mine" would be grammatically correct, but no one says it.

  – from Jay's answer to "my", "of me", "of mine" - when to use these possessive constructions

• I thought maybe it is short for That's a car of his [cars], but I have no way of making sure; it sounds a little odd that way to me.

  – from the question Why do we say "of mine/of his" instead of "of me/of him"?

Although interpreting "yours" as a plural possessive pronoun standing for "your husbands" seems plausible, I would actually say it is wrong.

I found a Language Log post that supports this point, "Genitive Anxiety". it has an interesting quote from the Merriam-Webster's Concise Dictionary of English Usage that cites a counterexample found in Tristam Shandy that Otto Jespersen pointed out: "this exactness of his," which cannot be turned into "one of the exactnesses of him."

I might be wrong, but I think the MWCDEU is correct that this is not a partitive construction. However, if you are curious about the arguments that have been made for the partitive analysis, one paper I found that supports the partitive view is English Partitives and Double Genitives, by Alya Asarina. I'm not especially convinced by the evidence it gives, but I'm not an expert.

What I would say is that, while a partitive construction may be the origin of this expression, in modern English "of mine/yours" etc. purely indicate possession. The construction "A(n) X of mine" with an indefinite article often indicates the existence of more than one X, but this interpretation is influenced by the presence of the indefinite article. Using the definite article the with a double genitive is not idiomatic because the established way of indicating a definite possessed object is to use a possessive pronoun like my, your, their as the determiner. But people don't seem to have any problem with combining the double genitive structure with other definite determiners than the, such as the demonstrative determiners this and that.

As for logic: sure, it's perfectly logical, as long as you consider it a construction of its own rather than trying to analyze it word-by-word. It's just as logical as the English perfect construction, which as BladorthinTheGrey's question mentions seems to derive ultimately from expressions of possession + the semantics of the past participle ("I have a broken pencil" ≈ "I have broken a pencil") but which cannot be analyzed this way today due to extension of the construction to other contexts, such as intransitive verbs ("I have fallen").

I'll try to address the logic. The construction is necessitated by the presence of both the demonstrative and the possesive construction. Noting that

*that your husband

is wrong (as both that and your are determiners), that husband of yours is really a workaround to include both the demonstrative and the possesive (rather than an attempt to refer to a pool of husbands).