Difficult Conditional Formatting

I am currently running Excel 2013. I have 1 workbook with 2 sheets. I have attached for reference. Here's what I am wanting to accomplish...

I want row 2 on "Summary" to be conditionally formatted green if the following 2 criteria are met...
1. a value is present in the row corresponding with the current month AND....
2. the current month is equal to the month defined in the "Date Due" column.

At the end of the current month, I would like for it to "reset" the conditional formatting and then look at row 3 (and so on...) based upon the current date.

I know this sounds rather complicated. Any help would be MOST appreciated!

Thank you!

Would you put some more data in your file and show us an example of the results you'd like to see?
Actually, in the Summary sheet, I only see "1st" as due date which is not really a date.
Thanks