Is this expression actually used commonly in Hungarian, or is it simply a literal translation of the phrase mi casa es su casa?
I don't know how often it is used but there is nothing wrong with using it in Hungarian. Another, possibly more common phrase is "Érezd magad otthon." - close to "Make yourself at home.".
There is nothing wrong with saying My house is your house in English, also, but it isn't frequently said either. It's much more likely you would hear Make yourself at home or even mi casa es su casa (it is such a common Spanish phrase that even English speakers will use it)
Although given the Hungarian sentence, shouldn't it be "Mi casa es tu casa? :)
I speak practically no Spanish, but I immediately thought of this Spanish saying which is known (at least to some extend) also in German.