Is it possible to use port 80 for both HTTP and web socket traffic?

YES, by using node.js. Express or connect for the HTTP file serving and socket.io for the WebSocket stuff.

Example:

var express = require("express");
var app = express.createServer(); 

app.get("https://stackoverflow.com/", function(req, res){ 
    res.redirect("/index.html");
}); 

app.configure(function(){
  app.use(express.static(__dirname + '/public'));
});

app.listen(80); 

var io = require('socket.io'); 
var socket = io.listen(app); 
socket.on('connection', function(client){ 
  client.on('message', function(){...});
})