carto - How does one use leaflet layergroups with CartoDB layers?

I'm trying to use leaflet layergroups with a cartodb layer, ala: http://leafletjs.com/reference.html#layergroup but haven't been able to successfully do it.

This is what I have so far:

    var map = new L.Map('map', {
      zoomControl: true,
      center: [41.460, -81.67],
      zoom: 11
    });

    map.locate({setView: true, maxZoom: 18});

    var background = L.tileLayer('http://{s}.tile.stamen.com/toner-lite/{z}/{x}/{y}.png', {

      attribution: 'Stamen',
      maxZoom: 15,
      errorTileUrl: 'http://fashiontech.files.wordpress.com/2008/08/plaid_b_single.jpg?w=256'
    })
     .setZIndex(0),

    cdb = cartodb.createLayer(map, 'http://cleveland-metroparks.cartodb.com/api/v2/viz/05af5a7c-668d-11e3-8914-cb7f69afe66f/viz.json')

     .on('done', function(layer) {


      layer.setInteraction(true);

      layer.on('featureOver', function(e, pos, latlng, data) {
        cartodb.log.log(e, pos, latlng, data);
      });

      layer.on('error', function(err) {
        cartodb.log.log('error: ' + err);
      });
    }).on('error', function() {

      cartodb.log.log("some error occurred");
    }),

    labels = L.tileLayer('http://{s}.tile.stamen.com/toner-labels/{z}/{x}/{y}.png', {
      attribution: 'Stamen',
      maxZoom: 18
    })
     .setZIndex(600);

    var existing = L.layerGroup([background, cdb]);

    var baseLayers = {
        "Existing": existing
    };        

    L.control.layers(baseLayers).addTo(map);

This answer hints that it's possible, but my js-fu is really lacking: How does Leaflet layer ordering work with CartoDB layers?