I think that adding title to the div is the only way for you to do a background image in CSS.

You can cheat a little by then loading a transparent image in the container that the background image is in, make this transparent image have an alt tag and title tag for whatever your background image is about.

If you are doing this for seo purposes this should work, if you are doing it to have the html well formatted, there is only the div tag.

Cheers!
-Erick

Yes for screen readers and using it as alt and title for your images that are there. So you are not trying to trick Google, you are trying to figure out a way to mark what is actually there. For google image search, I have had success ranking images even if used as backgrounds in divs by naming them with what I was trying to rank them for. Since I could not use alt or title I named images with my target in them. These images were all for a brand query.

Example: image on mybrand.com named mybrand-imageName.png

we were able to get most of those images to show up when doing an image search for mybrand