Make div expand to occupy available height of parent container

Answer 1

I would try another aproach. Using jquery you can calculate on window load the height of the highest h3 and then, apply that height to all your h3 inside your tiles.

I know you asked for a pure css solution, so it's ok if I don't get any credit, but I think this answer may be usefull for other users with the same problem so that's why I wrote it.

Something like this:

var maxHeight = -1;
$('.tile h3').each(function() {
    if ($(this).height() > maxHeight)
        maxHeight = $(this).height();
});
$('.tile h3').each(function() {
    $(this).height(maxHeight);
});

As you can see in this JSFIDDLE (notice I removed the fixed max-heightyou added to the header and add a third tilewith a "very long text" so you can check the exmaple better.