We consider an optical medium consisting of a periodic refractive-index gra
ting and a periodic set of thin layers of two-level systems resonantly inte
racting with the electromagnetic field. Recently, it has been shown that su
ch a system gives rise to a vast variety of stable bright solitons. In this
work, we demonstrate that the system has another very unusual property: st
able bright solitons can coexist with stable continuous-wave (cw) states an
d stable dark solitons (DS's). Depending on the parameters' values, a DS fr
equency band coexists (without overlap) with one or two bright-soliton band
s. Quiescent (standing) DS's are found in an analytical form, and moving on
es are obtained numerically. Simulations show that a considerable part of t
he DS solutions are completely stable against arbitrary small perturbations
. The fact that this system supports both stable bright and dark solitons f
or the same parameters values may find interesting applications in photonic
s. [S1063-651X(99)13311-7].