Three.js / WebGL - transparent planes hiding other planes behind them

Setting the depthWrite property to false solved my issue.

new THREE.MeshBasicMaterial({ 
    opacity: 0.25, 
    transparent: true, 
    side: THREE.DoubleSide, 
    depthWrite: false
});

Let's say that you are using some transparent *.png image. Then this would help:

new THREE.MeshBasicMaterial( { side:THREE.BackSide,map:texture, depthWrite: false, depthTest: false });