In this paper, we study the class of a BH lattices as a common frame to Brouwerian and Heyting lattices and investigate some related properties. Also, we characterize the divisibility condition in the definition of BH lattice and we obtain that the set H of all idempotent elements in a BH lattice $L$ forms a Heyting algebra. We introduce the notion of an IBH lattice and under some specific conditions, we characterize an MV algebra, a bounded Wajsberg hoop, a Boolean Algebra, and a commutative bounded BCK algebra in terms on IBH lattices.