Chances are the client is merely asking for what they think is used. Some colleague or friend told them "Make certain they give you the .psd." So they ask for that. I would hesitate to state you needed to do so, especially for a website, if there is no .psd. A better course may be to explain why there is no .psd file and how much more versatility there is without it.
I get clients asking me for the ".psd" all the time, even for 56 page catalogs. They don't fully understand that other things besides Photoshop are used. I always take the opportunity to politely educate them a bit as to why I'm more than merely a Photoshop hobbyist and the breadth and scope of the tools in my toolbox :)
The only thing I know of...
For a Mac.
Page Layers is a website screenshot app for Mac OS X. It converts web pages to Photoshop files with separate layers for all page elements.
Just open any page in the embedded browser and save the page as PSD with layers or as plain PNG image. Every web page element (every image, link, block, ...) will be rendered as separate, named layer. Layer groups will be created according to the site structure.
I have no idea if there's anything similar for Windows.
I am not affiliated with the link at all, just use the product when needed.