The notions of a $mathcal{N}$-subalgebra, a (strong) $mathcal{N}$-ideal of BH-algebras are introduced, and related properties are investigated. Characterizations of a coupled $mathcal{N}$-subalgebra and a coupled (strong) $mathcal{N}$-ideals of BH-algebras are given. Relations among a coupled $mathcal{N}$-subalgebra, a coupled $mathcal{N}$-ideal and a coupled strong $mathcal{N}$ of BH-algebras are discussed.