Van der Waals heterostructures obtained via stacking and twisting have been used to create moiré superlattices1, enabling new optical and electronic properties in solid-state systems. Moiré lattices in twisted bilayers of transition metal dichalcogenides (TMDs) result in exciton trapping2-5, host Mott insulating and superconducting states6 and act as unique Hubbard systems7-9 whose correlated electronic states can be detected and manipulated optically. Structurally, these twisted heterostructures feature atomic reconstruction and domain formation10-14. However, due to the nanoscale size of moiré domains, the effects of atomic reconstruction on the electronic and excitonic properties have not been systematically investigated. Here we use near-0°-twist-angle MoSe2/MoSe2 bilayers with large rhombohedral AB/BA domains15 to directly probe the excitonic properties of individual domains with far-field optics. We show that this system features broken mirror/inversion symmetry, with the AB and BA domains supporting interlayer excitons with out-of-plane electric dipole moments in opposite directions. The dipole orientation of ground-state Γ-K interlayer excitons can be flipped with electric fields, while higher-energy K-K interlayer excitons undergo field-asymmetric hybridization with intralayer K-K excitons. Our study reveals the impact of crystal symmetry on TMD excitons and points to new avenues for realizing topologically non-trivial systems16,17, exotic metasurfaces18, collective excitonic phases19 and quantum emitter arrays20,21 via domain-pattern engineering.