You can set up something like the following in your list's Custom HTML -> Subscribe Success page:
<html>
<head>
<meta http-equiv="refresh" content="2; URL=http://yoursite.com/mysignup.html">
</head>
<body>
<a href="http://yoursite.com/mysignup.html">Click here</a> if you are not redirected in 2 seconds
</body>
</html>
There is also a way to forward the message codes, available in Custom HTML, to your page:
<html>
<head>
<meta http-equiv="refresh" content="2; URL=http://yoursite.com/mysignup.html?e=!email&fn=!fname">
</head>
<body>
<a href="http://yoursite.com/mysignup.html?e=!email&fn=!fname">Click here</a> if you are not redirected in 2 seconds
</body>
</html>
Hope that helps!
Regards