Recently I started to try out Windows 8 Phone Development using Visual Studio 2012 express and the Windows 8 Phone SDK, when using HTML5 template I ran into this problem which I reported on stackoverflow, here is how I solved it :

Step 1 : Add jquery.min.js to the solution

Step 2 : Change the order of statement in Browser_Loaded method as shown below

private void Browser_Loaded(object sender, RoutedEventArgs e)
    // Add your URL here
    Browser.IsScriptEnabled = true;
    Browser.Navigate(new Uri(MainUri, UriKind.Relative));

Step 3: Sample Jquery code

<!DOCTYPE html>
        <meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
        <link rel="stylesheet" type="text/css" href="/html/css/phone.css" />
        <script type="text/javascript" src="/html/js/jquery.min.js" ></script>
        <title>Windows Phone</title>
      <script type="text/javascript">
        $(document).ready(function () {
          $("#message").text("Welcome !");

            $("#message").text("button has been pressed");
            <p>MY APPLICATION</p>
        <div id="message"></div>
        <input type="button" id="goBtn" value="press me !" />


Hope this helps you :)