so... does "... between you and I" have 2 subjects?
Unfortunately, many people are terrified of using objective case where subjective case should be used (but not the reverse) so have not understood which belongs where, and the first person subjective is being used more and more in informal speech (even worse, the reflexive, in such constructions as "They gave a present to Jan and myself." Shudder.) But still, at this point, the objective case exists and is in use especially in writing.
In your example, "This is between you and me," (the correct form), what governs the case of the personal pronouns is the preposition "between." Prepositions take objects, not subjects. (Prepositions include to, from, among, between, before, after, etc.) The confusion usually arises with the verb "to be" which, in formal speech (but not everyday speech) does not take an object: "It is I" and "That was she on the phone" are correct. But if you add in a preposition, then it's back to objective: "Give it to me" or "I bought it from her" or "The tickets were handed to them by a stranger."
When faced with a compound subject or object such as "He and I" or "you and me", use either a singular first-person pronoun alone, or the plural form to check if you're not sure whether you need an object or subject. "This is between us" is correct; "This is between we" is clearly not. You need the objective...and so "This is between you and me" is correct. "This" is the subject. Since "is" doesn't take an object, "between you and me" defines a location of action (in this case a limit to sharing information) and the preposition is the reason for the objective case.
But yes, again, it would be I. 
