Interacting selectively and non-covalently with the Bcl-2 homology (BH) domain of a protein. Bcl-2-related proteins share homology in one to four conserved regions designated the Bcl-2 homology (BH) domains BH1, BH2, BH3 and BH4. These domains contribute at multiple levels to the function of these proteins in cell death and survival. Anti-apoptotic members of the Bcl-2 family have four BH domains (BH1-BH4). Pro-apoptotic members have fewer BH domains.