I have some USB flash drives that I'd like to image - just in case I screw
them up or lose them - but I can't find any software that backs up USB flash
drives as complete images.

Some of my drives have several partitions, so the USB drive needs to be
imaged completely - just like you can do with an internal hard drive.

I have Acronis True Image Home 11 but it won't even see the USB flash
drives.

Have you seen software used to image USB drives?

jim