test manual height calculations
I had the exact same issue working on a project. It ended up that the best trick to end up with a cross-browser solution was actually absolute positionning.
.wrap{background:pink;position:absolute;top:0;left:0;right:0;bottom:0}
You are allowed to be sceptical, but have a look at this jsfiddle ;)
http://jsfiddle.net/evomk0zu/