I'm not realy clear what you mean with a "nested solution".
is the "main page" of your application.
If there is a directory http://mysite.com/Assets/Images
than your first approach ~/Assets... would work.
would be the main page you can't reach
The simpliest way to solve your problem is:
a.) create an aspx page with a textbox and a button on it
b.) In the (server) click handler of the box try to translate the text of your textbox with MapPath and ResolveUrl
--check whats comming out via debug - or add an extra control to set the value.
Be sure that you create the page in your "nested solution".
ResolveUrl for an example would translate ~/default.aspx to /default.aspx if your app is "rooted" if not it maybe translated to something like /MyApp/default.aspx.
If you can translate your path finally - you should have the solution for the problem - or in other words the value you have to set in file explorer.