To do that you would need to use both directions of browser communication. Here is one example of how it could be done:

using UnityEngine;
using System.Collections;

public class WebCheck : MonoBehaviour
{
    private string m_Address;

    public void ResolvePageAddress ()
    {
    	Application.ExternalEval ("GetUnity ().SendMessage ('WebCheckGameObject', 'SetPageAddress', document.location);");
    	Debug.Log (m_Address);
    }

    public void SetPageAddress (string address)
    {
    	m_Address = address;
    }
}

For this script example to be working, your script would need to be in the scene on a GameObject by the name "WebCheckGameObject".

try Application.dataPath it doesn't return the exact html file, but it does return the path. If you're going for antipiracy this should be enough. For example:

if (Application.platform == RuntimePlatform.WindowsWebPlayer || Application.platform == RuntimePlatform.OSXWebPlayer)
{
    datapath = Application.dataPath;
    if(datapath == "http://mypage.com/games/mygame")
    {
    	print("This is the correct page. No piracy detected.");
    }
    else
    {
    	print("Dr Jones: This game doesn't belong on this webpage. It BELONGS IN A MUSEUM!\nAuctioneer:SIT DOWN Dr Jones!");
    }
}

Check out the Unity function Application.absoluteURL. The Scripting Reference for that function also has an anti-piracy code sample using that and Application.dataPath.