We studied the phase transitions, domain morphologies, and polarizations in BaTiO(3)/SrTiO(3) superlattices grown on SrTiO(3) substrates. Using the phase field approach, we discovered the remarkable influence of film/substrate interfacial coherency on the ferroelectricity of the SrTiO(3) layers within a superlattice: it is an orthorhombic ferroelectric for an incoherent interface while it exhibits only induced polarization by the adjacent BaTiO(3) layers for a coherent interface. We presented the domain morphologies within individual BaTiO(3) and SrTiO(3) layers which have different ferroelectric symmetries. The results are compared to ultraviolet Raman spectroscopy and variable temperature x-ray diffraction measurements.