You usually wouldn't use genitive, though, but dative: "Die Filmnacht meiner Freundin und mir" (the movie night [of] mine[gen.] gf and me[gen.]). Which a bit confusingly turns into straight nominative in English, "The movie night of my gf and I", I'm usually very insistent on putting objective everywhere I can but "the movie night of whom" really doesn't sound right. Don't ask me why do I look like a linguist.

Alternatively, sufficiently nordic, "Meiner Freundin und mir unsere Filmnacht", which'd be "mine gf and I our movie night"... by proxy via "Mien leevste un ik uns Filmnacht", that is, Low Saxon, where the construction comes from. Trying to match the Standard German rendering up with English case-wise is breaking my brain. Low Saxon has the exact same case structure as English so I'm declaring it correct. Or is it "un mi" / "and me"? It shouldn't. But I've spent way too much time thinking about it so now I'm unsure.