How can I overlap two images replacing the upper values to the lower?

I want to create a photo montage, overlaying two images of the same size already placed at the correct final position. The two matrix are formed by 0-values except for the two images that I want overlay. The difficulty is that the upper image partially overlay the first image. So what I would like to obtain is a sort of sum of the values of the two matrix where the two images don't overlay, and a replacement of the values of the lower image with those one of the upper image where the images overlay. Thank you Alice