Interacting selectively and non-covalently with the BH1 domain of a protein of the Bcl-2 family. Proteins that act as inhibitors of apoptosis harbour at least three BH domains: BH1, BH2 and BH3; the BH1 and BH2 domains are found in all death antagonists of the Bcl-2 family but only in one class of death agonists.