An example using WMS in mapbox.js

<!DOCTYPE html>
<html>
<head>
<meta charset=utf-8 />
<title></title>
  <script src='//api.tiles.mapbox.com/mapbox.js/v1.3.1/mapbox.js'></script>
  <link href='//api.tiles.mapbox.com/mapbox.js/v1.3.1/mapbox.css' rel='stylesheet' />
  
  <style>
    body { margin:0; padding:0; }
    #map { position:absolute; top:0; bottom:0; width:100%; }
  </style>
</head>
<body>
<style>
  #map-ui {
    position:absolute;
    top:10px;right:10px;
    z-index:100;
    }
    #map-ui ul {
      list-style:none;
      margin:0;padding:0;
      }
      #map-ui a {
        font-size:13px;
        background:#FFF;
        color:#3C4E5A;
        display:block;
        margin:0;padding:0;
        border:1px solid #BBB;
        border-bottom-width:0;
        min-width:138px;
        padding:10px;
        text-decoration:none;
        }
      #map-ui a:hover { background:#ECF5FA; }
      #map-ui li:last-child a {
        border-bottom-width:1px;
        -webkit-border-radius:0 0 3px 3px;
                border-radius:0 0 3px 3px;
        }
      #map-ui li:first-child a {
        -webkit-border-radius:3px 3px 0 0;
                border-radius:3px 3px 0 0;
              }
      #map-ui a.active {
        background:#3887BE;
        border-color:#3887BE;
        color:#FFF;
        }
        #map-ui li:last-child a.active {
          border-top-color:#FFF;
          }

</style>
<div id='map'>
	<div id='map-ui'>
    <ul>
      <li><a href='#' class='active' id='images'>VCGI Imagery</a></li>
      <li><a href='#' class='active' id='precipitation'>Precipitation</a></li>
    </ul>
  </div>
</div>
<script>
var map = L.mapbox.map('map', 'examples.map-y7l23tes')
    .setView([44, -72.5], 7);

var images = L.tileLayer.wms("https://maps.vcgi.org/arcgis/services/EGC_services/IMG_VCGI_BW_WM_CACHE/ImageServer/WMSServer", {
    format: 'img/png',
    transparent: true,
    layers: 1
}).addTo(map);

var precipitation = L.tileLayer.wms("https://nowcoast.noaa.gov/wms/com.esri.wms.Esrimap/obs", {
    format: 'image/png',
    transparent: true,
    layers: 'RAS_RIDGE_NEXRAD'
}).addTo(map);

var topPane = map._createPane('leaflet-top-pane', map.getPanes().mapPane);
var topLayer = new L.mapbox.tileLayer('landplanner.map-6loa9k8g', {
	maxZoom: 17
}).addTo(map);
topPane.appendChild(topLayer.getContainer());
topLayer.setZIndex(7);

// Layer switcher
document.getElementById('images').onclick = function () {
    var enable = this.className !== 'active';
    images.setOpacity(enable ? 1 : 0);
    this.className = enable ? 'active' : '';
    return false;
};

document.getElementById('precipitation').onclick = function () {
    var enable = this.className !== 'active';
    precipitation.setOpacity(enable ? 1 : 0);
    this.className = enable ? 'active' : '';
    return false;
};
</script>
</body>
</html>

https://api.tiles.mapbox.com/mapbox.js/v1.3.1/mapbox.js