  The compound Sr$_{0.5}$Ce$_{0.5}$FBiS$_{2}$ belongs to the intensively
studied family of layered BiS$_2$ superconductors. It attracts special
attention because superconductivity at $T_{sc} = 2.8$ K was found to coexist
with local-moment ferromagnetic order with a Curie temperature $T_C = 7.5$ K.
Recently it was reported that upon replacing S by Se $T_C$ drops and
ferromagnetism becomes of an itinerant nature (Thakur et al., Sci. Reports 6,
37527 (2016)). At the same time $T_{sc}$ increases and it was argued
superconductivity coexists with itinerant ferromagnetism. Here we report a muon
spin rotation and relaxation study ($\mu$SR) conducted to investigate the
coexistence of superconductivity and ferromagnetic order in
Sr$_{0.5}$Ce$_{0.5}$FBiS$_{2-x}$Se$_x$ with $x=0.5$ and $1.0$. By inspecting
the muon asymmetry function we find that both phases do not coexist on the
microscopic scale, but occupy different sample volumes. For $x=0.5$ and $x=1.0$
we find a ferromagnetic volume fraction of $\sim \, 8 \%$ and $\sim \, 30 \%$
at $T=0.25$ K, well below $T_{C} = 3.4$ K and $T_C = 3.3$ K, respectively. For
$x=1.0$ ($T_{sc} = 2.9$ K) the superconducting phase occupies the remaining
sample volume ($\sim \, 70 \%$), as shown by transverse field experiments that
probe the Gaussian damping due to the vortex lattice. We conclude
ferromagnetism and superconductivity are macroscopically phase separated.
