I don't know when the husband has called. > I don't know when the husband called.

Maybe even: I don't know when her husband called.

I don't know the other languages, so I'm not sure about "the" versus "her," but "has" shouldn't be there.

It is not clear whose husband has not called.
What's wrong with has called?

It sounds unnatural in English. Using the past perfect tense with clauses using question words (when/where/etc.) gives it a subjuctive mood: "Let me know when he has called."
In this situation, the event has clearly occured already, and so it sounds strange to a native.

Past perfect means that the event has clearly occurred already. That is the meaning of the word perfect. It does sound unnatural, only because people tend to make shortcuts whenever possible.

I am not enough of an English expert to say if it is 100% grammatically sound or not. However, the fact remains that a native English speaker would not write or say this sentence with "has" in it. In my opinion, it is misleading to someone learning English, as it may confuse them about the usage of "has called."

technically, abbia chiamato (present perfect) translates to has called.
There are only two options:
1. either "has called" is identical to "called" or
2. "has called" has a different meaning altogether.
I believe they are identical, so I choose the former. There is no objection to introduce another variant.

I did finally come with a situation where someone might actually say it the way you have it.

Someone knows that the husband has called multiple times, but they are unsure of the exact times that he had called.

Right, we know WHY you have chosen the wording, and in Italian it is correct prescriptively as well as descriptively. Having spoke English all my life, I understand this type of clause "when/where/etc....(past perfect)" as being in the subjunctive mood rather than indicative past perfect (as you have intended). Language is not always logical; it does not always follow prescriptive rules, and I agree that it may be misleading to someone learning English.

I could see a receptionist at a hospital or nursing home saying "the husband," but yes, it would be much less common.