Unexpected ambient light effect.

In the following code, I make several cubes and tan them with PointLight and AmbientLight. However, when set to 0xffffff, AmbientLight changes the color of the sides to white, regardless of their assigned colors. Oddly enough, spotlight works as expected.

How can I make the surrounding light behave like a point light, since it should not wash out complexions, just illuminate them? That is why setting the ambient light to 0xffffff will be equivalent to having multi-point lights at full intensity around the object.

$(function(){
    var camera, scene, renderer;
    var airplane;
    var fuselage;
    var tail;
    init();
    animate();

    function init() {
        scene = new THREE.Scene();
        camera = new THREE.PerspectiveCamera( 35, window.innerWidth / window.innerHeight, 0.1, 10000 );
        camera.position.z = 2;

        airplane = new THREE.Object3D();
        fuselage = newCube(
                {x: 1, y: 0.1, z: 0.1}, 
                {x: 0, y: 0, z: 0},
                [0xffff00, 0x808000, 0x0000ff, 0xff00000, 0xffffff, 0x808080],
                [0, 1, 2, 3, 4, 5]
        );
        airplane.add(fuselage);
        tail = newCube(
                {x: 0.15, y: 0.2, z: 0.05}, 
                {x: 0.5, y: 0.199, z: 0},
                [0xffff00, 0x808000, 0x0000ff, 0xff00000, 0xffffff, 0x808080],
                [0, 1, 2, 3, 4, 5]
        );
        airplane.add(tail);
        scene.add( airplane );

        var ambientLight = new THREE.AmbientLight(0xffffff);
        scene.add(ambientLight);        

        var pointLight = new THREE.PointLight(0x888888);
        pointLight.position.x = 100;
        pointLight.position.y = 100;
        pointLight.position.z = 100;
        scene.add(pointLight);      

        renderer = new THREE.WebGLRenderer();
        renderer.setClearColorHex(0x000000, 1);
        renderer.setSize( window.innerWidth, window.innerHeight );
        document.body.appendChild( renderer.domElement );
    }

    function animate() {
        requestAnimationFrame( animate );
        render();
    }
    function render() {
        airplane.rotation.x += 0.005;
        airplane.rotation.y += 0.01;
        renderer.render( scene, camera );
    }
});

function newCube(dims, pos, cols, colAss){
    var mesh;
    var geometry;
    var materials = [];
    geometry = new THREE.CubeGeometry( dims.x, dims.y, dims.z );
    for (var i in cols){
        materials[i] = new THREE.MeshLambertMaterial( { color: cols[i], overdraw: true } );
    }
    geometry.materials = materials;
    for (var i in colAss){
        geometry.faces[i].materialIndex = colAss[i];
    }
    mesh = new THREE.Mesh( geometry, new THREE.MeshFaceMaterial( materials ) );
    mesh.position = pos;
    return mesh;
}