  We report the first measurements of the effective superfluid density n_S(T)
\propto \lambda^{-2}(T) of Superconductor-Ferromagnet (SC/FM) bilayers, where
\lambda is the effective magnetic field penetration depth. Thin Nb/Ni bilayers
were sputtered in ultrahigh vacuum in quick succession onto oxidized Si
substrates. Nb layers are 102 A thick for all samples, while Ni thicknesses
vary from 0 to 100 A. T_C determined from \lambda^{-2}(T) decreases rapidly as
Ni thickness d_Ni increases from zero to 15 A, then it has a shallow minimum at
d_Ni \approx 25 A. \lambda^{-2}(0) behaves similarly, but has a minimum several
times deeper. In fact, \lambda^{-2}(0) continues to increase with increasing Ni
thickness long after T_C has stopped changing. We argue that this indicates a
substantial superfluid density inside the ferromagnetic Ni films.
