It's a rule in English that "and I" is only used when it's the subject not the object of a sentence. (Subject is the thing doing the action, and the object is the thing being acted upon)
The proper way to say this would be "she's coming over me and my girlfriend's movie night" because "she" is the subject in this sentence since she is the one "coming over".
Thanks for the explanation. I don't know if I'll really change my habit though. It's been ingrained into me over and over from a young age on that the "ass (donkey) always names themselves first" and it's a bit uncomfy to do so now. I also mostly don't feel bad about breaking that rule as it seems a bit arbitrary.
fake nerd, real nerds recognize that linguistic prescriptivism is poopoo and you can use language however you want, optionally in such a way that people understand what you're saying.
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.
when you say something belongs to you, you don't call it "I's thing" - you call it "my thing".
if it belongs to your friends Jim and Bob, it's "Jim and Bob's thing" or "Jim's and Bob's thing". likewise, when it belongs to your gf and yourself, it makes more sense to say "my gf and my" or "my gf's and my", rather than inventing a brand new word that sounds so very stupid.