Overlapping genetic information in eukaryotes
You might be interested in the INK4A locus (chromosome 9p), encoding both p19 and p16 genes, very close to p15. You can read a description here. All three proteins are known experimentally to exist. 

Now, whether these are two different genes or the same gene with alternative splicing and start sites leading to different reading frames it's up to discussion. The point is that p19 and p16 share DNA coding sequence but not protein sequence nor function.