  We study two colored operads of configurations of little $n$-disks in a unit
$n$-disk, with the centers of the small disks of one color restricted to an
$m$-plane, $m<n$. We compute the rational homotopy type of these \emph{extended
Swiss Cheese operads} and show how they are connected to the rational homotopy
types of the inclusion maps from the little $m$-disks to the little $n$-disks
operad.
