Multiple Criteria with VLookups/Indexs - Won't work?

I'm not sure whether it's the fact that I'm using two separate sheets or the fact that I'm attempting to select the entire column instead of a set number of rows, but this formula isn't working. I've looked up so many guides it hurts my head, so I hope someone can make this work for me and I can reverse-engineer the thing.

I'm looking for a formula to look up Column C's value (on Sheet 2) based on criteria from Column A and Column B (on Sheet 1).

Sheet 1
Col. A - Col. B - Col. C
John - 10/hr -
Mary - 15/hr - Lookup Formula goes here
Mary - 10/hr -

Sheet 2
Col. A - Col. B - Col. C
Mary - 10/hr - Regular
John - 10/hr - Regular
Mary - 15/hr - Overtime

So when it's done, sheet 1 will look like:

John - 10/hr -
Mary - 15/hr - Overtime
Mary - 10/hr -

Can someone please give me a formula for that? Thank you so much!

Thank you for your assistance Spencer, but I'm having an issue. I attempted to recreate the formula in my actual sheet (which links to a separate file, rather than a separate sheet, but I don't think it should be an issue) and it ends up returning "N/A" or an error. I'm using Ctrl+Shift+Enter to no change. I've tried selecting the entire column ( inwhat is effectively "Sheet 2" for me), I've tried selecting only part of the column, and still nothing. The data I'm looking up definitely matches (aside from font and text color) and is present on "Sheet 2", and a simpler VLookup that only tries to pull up based on one criteria works fine. Here is the code I'm posting... I've been trying to reverse engineer yours, but to no avail. Maybe you can explain a little more for me. :/

=INDEX([SpreadsheetUpdater.xls]report!$C:$C,MATCH(1,([SpreadsheetUpdater.xls]report!$B:$B=G3)*([SpreadsheetUpdater.xls]report!$A:$A=H3),0))

It returns an N/A.

I'm also fine with using Helper Columns. This is my first time ever hearing of them, but I'm willing to try anything to get this to work. Thanks.

Hmm, I think Helper Columns might actually do it; it will be inelegant, but simple. Thank you Spencer.

But can you still walk me through making that Index formula work, maybe from the start? I've provided the cells I'll be using in the other sheet in the formula above. I've tried entering it in from scratch, character for character, cell for cell, and I just couldn't get it to work. Trust when I say I'm not an idiot with this sort of thing, and if I still don't get it after this, I'll just drop it and walk, but I'm just looking for a little step-by-step instruction.