Are DUPLO blocks compatible with LEGO blocks in any way? Can I build a model out of both DUPLO blocks and LEGO blocks? Do they fit together?
Yes! You can add LEGO on top of DUPLO, and DUPLO on top of LEGO. Here's an example picture from The Brick Blogger:



Because stacking LEGO on top of DUPLO requires the particular LEGO tube design on the bottom (to fit in the hollow top of the DUPLO bricks), many "LEGO-compatible" bricks do not share this compatibility with DUPLO - at best, you can stack DUPLO on top of them, but not the other way around.

In addition, you can use only some types of LEGO bricks with DUPLO. Plates, tiles and other modified pieces can't stack with DUPLO. DUPLO can sit happily on top of plates, but plates and tiles only balance on top of Duplo, there's no real clutch between them that way.