Make div expand to occupy available height of parent container

Answer 1

How about a fixed height:

.tile h3 {
    height: 65px;
    display: inline-block;
    overflow: hidden;
}

Or accompanied by js (jQuery):

// Height handler
var headHeight = 0;

// Iterate throug all H3s an get highest
jQuery( 'h3' ).each( function() {

    // Get current height
    var currentHeight = jQuery( this ).height();

    // If higher as handler set as handler
    if( currentHeight > headHeight ) {
        headHeight = currentHeight;   
    }

} );

// Set the height of all H3s
jQuery( 'h3' ).css( 'height', headHeight );

This would be a pretty robust solution ...