We have measured the evolution of the tunneling density of states (DOS) in superconductor/ferromagnet (S/F) bilayers with increasing F-layer thickness, where F in our experiment is the strong ferromagnet Ni. As a function of increasing Ni thickness, we detect multiple oscillations in the DOS at the Fermi energy from differential conductance measurements. The features in the DOS associated with the proximity effect change from normal to inverted twice as the Ni thickness increases from 1 to 5 nm.