We analyze the local density of states (LDOS) of heterostructures consisting of alternating ferromagnet, F, and superconductor, S, layers. We consider structures of the SFS and SFSFSFS type, with thin nanometer scale F and S layers, within the ballistic regime. The spin-splitting effects of the ferromagnet and the mutual coupling between the S regions, yield several nontrivial stable and metastable pair amplitude configurations, and we find that the details of the spatial behavior of the pair amplitude govern the calculated electronic spectra. These are reflected in discernible signatures of the LDOS. The roles that the magnetic exchange energy, interface scattering strength, and the Fermi wavevector mismatch each have on the LDOS for the different allowed junction configurations, are systematically investigated.