How can I avoid digesting protein-bound DNA?
Well, it depends if you just want to sequence your protein bound fragments.
If that is the case, I suppose you could go for a FAIRE-seq.
Basically, you perform several iterative phenol/chlo extractions, thus separating the bound and unbound fragments.
Then you sequence the unbound fragments that are present in the aqueous phase, and after the mapping, you can deduce the regions that were actually bound to proteins.

I don't know if it is possible to treat your bound fragments (that you isolate after a phenol/chlo extraction in the organic phase) with proteinase K, then perform another phenol/chlo extraction to purify your formerly bound fragments and sequence them. 
Could be worth trying.