Count rows based on three criteria, including blank cell

I have three columns, the first two contain a date, the third one a number or a blank cell.
I am trying to count all the rows in those columns where a date (in D3) falls between the dates in the first two columns and the third column contains an empty cell.

At the moment my formula looks like this:


I have also tried:


The first two critera seem to work, but as soon as I add the third one (check for empty cell) the result is always 0.

I think no option for use a function inside COUNTIFS() function, but it easy to do with SUMPRODUCT():


Thanks that really helped. It works, though it seems a little unintuitive, I would never have worked out by myself to use this function for what I was trying to do.