You have to set the height for the parents (container and child) explicitly, here is another work-around (if you don't want to set that height explicitly):
.child {
width: 30px;
background-color: red;
display: table-cell;
vertical-align: top;
position:relative;
}
.content {
position:absolute;
top:0;
bottom:0;
width:100%;
background-color: blue;
}