parents..., they're destroying my relationship... not to mention my life Options

[elaboratedream]

so, I've been going out with my girlfriend for about a month and a week now.

and right now, she's thinking about breaking up with me... not for anything I did, but because of my parents.
My parents have always been overprotective. I went to a small Catholic school from kindergarten until 8th grade and now that I'm in a public highschool, they're having issues with accepting that I have new friends. They're used to knowing all my friends and thier parents really well.
It's really hard because they dont want me hanging out with people they dont know... and there's no way they can get to know them if they're gonna be doing that. I've tried to have people over, and I had my gf over once and she didnt do anything that would cause my parents to not like her... or at least I didnt think so.

I've been trying to hang out with her more, but my parents dont want me to. They seem to think she's "a troublemaker"...

and this is really putting a strain on our relationship because I can only see her at school... and thats not very much... a total of about 15 minutes a day.

I'm starting to wonder if maybe my parents have figured out that I'm not straight... I suppose that would partially explain things.
They're homophobes and besides that, they dont want me dating until I'm 16 or 17 either. (i'm 15 right now)

I really dont want to lose my gf over something like this... how can I figure out why my parents dont want me hanging out with her and how can I convince my parents to let me hang out with her more?