  We construct gravitational solutions that holographically describe two
different $d=4$ SCFTs joined together at a co-dimension one, planar RG
interface and preserving $d=3$ superconformal symmetry. The RG interface joins
$\mathcal{N}=4$ SYM theory on one side with the $\mathcal{N}=1$ Leigh-Strassler
SCFT on the other. We construct a family of such solutions, which in general
are associated with spatially dependent mass deformations on the
$\mathcal{N}=4$ SYM side, but there is a particular solution for which these
deformations vanish. We also construct a Janus solution with the
Leigh-Strassler SCFT on either side of the interface. Gravitational solutions
associated with superconformal interfaces involving ABJM theory and two $d=3$
$\mathcal{N}=1$ SCFTs with $G_2$ symmetry are also discussed and shown to have
similar properties, but they also exhibit some new features.
