You can achieve this using a custom dialog (public class MenuDialog extends Dialog) that is semi-transparent (use alpha value in your bg color like #88000000). Set its content view to any XML layout you like, include a WebView if you want.
And in the constructor, you probably could put something like:
Window window = getWindow();
window.setFlags(WindowManager.LayoutParams.FLAG_LAYOUT_NO_LIMITS,
WindowManager.LayoutParams.FLAG_LAYOUT_NO_LIMITS);
window.requestFeature(Window.FEATURE_NO_TITLE);
window.setGravity(Gravity.BOTTOM);
window.setBackgroundDrawable(
context.getResources().getDrawable(android.R.color.transparent) );