Balanced categories with pullbacks have strong monomorphisms

In a balanced category with pullbacks in a category, pull a monomorphism back across the bottom map of a lifting square whose left map is an epimorphism. The resulting monic projection is epic because its composite with the lifted top map is epic. Balancedness makes that projection invertible, producing the unique lift. Conversely, if all monomorphisms are strong monomorphisms, applying the lifting property of a bimorphism to its own square gives its inverse, so the category is balanced. Pullback stability of epimorphisms is not needed.