In standard dictionaries the preposition collocated with ,,sich unterhalten'' is ,,über'', hence ,,sich unterhalten über etw.'' is definitely correct.
On the other hand, I am wondering whether ,,sich unterhalten von etw.'' could be a possible alternative, in analogy to the cases of ,,sprechen/reden'' :
von/über etw. sprechen
von/über etw. reden
No. It is sich über etwas unterhalten. Always. von is definitely wrong in this context.
You can
where unterhalten has complete different meanings in those two cases.
The verbs reden and sprechen can be used transitive and intransitive, but not reflexive:
intransitive (without accusative object)
Jetzt rede ich!
Jürgen redet mit Helga.
Hans redet von dir, nicht von Julia.
Anna redet nich gerne über ihre Eltern.
(All Examples work also with sprechen instead of reden.)
transitive (with accusative object)
Heinz spricht Deutsch.
Du redest nur Müll.
reflexive (with a reflexive pronoun, i.e. mich/dich/sich/uns/euch)
Wrong:
Ich spreche mich ...
There is just an idiom in which reden is used reflexive: »Er redet sich um Kopf und Kragen.« But this is an exception. Normally you don't use reden or sprechen reflexive.
The Verb unterhalten has more than one meanings. Think of each meaning as a different word.
jemanden unterhalten = to entertain somebody
Die Akrobaten unterhielten das Publikum im Zirkuszelt.
The acrobats entertained the audience in the circus tent.
In this meaning unterhalten is used transitive (i.e. with an accusative object)
sich mit jemandem unterhalten = to talk with somebody
Jürgen unterhielt sich mit Helga über den gestrigen Vorfall.
Jürgen talked with Helga about yesterday's incident.
In this meaning unterhalten is always used reflexive (with a reflexive pronoun) and with a prepositional object (»mit« + dative object).
sich unterhalten = to be amused
Ich habe gestern ein Kabarett besucht, ich habe mich köstlich unterhalten.
I visited a comedy show yesterday, I was very amused.
In this meaning unterhalten is always used reflexive (with a reflexive pronoun) but without any other object.
jemanden unterhalten = to support a person (financially)
Kein Wunder, dass er mit dem Geld nicht auskommt. Herr Mayer unterhält gleich drei Geliebte.
No wonder he does not manage with the money. Mr. Mayer has three lovers.
In this meaning unterhalten is used transitive (i.e. with an accusative object)
etwas unterhalten = to maintain
Die Römer unterhielten enge Kontakte zu den Etruskern.
The Romans maintained close contacts with the Etruscans.
In this meaning unterhalten is used transitive (i.e. with an accusative object)
The meaning you had in mind with your question, is #2 in the list above. There are two patterns that you can use with this verb:
in (2) the parts »mit <Person B>« and »über <Thema>« are both prepositional objects. The Object starting with mit is mandatory, the Object starting with über is optional.
