The objective of this paper is two-fold: firstly, we develop a localand global (in time) well-posedness theory for a system describing the motionof two fluids with different densities under capillary-gravity waves in a deepwater flow (namely, a Schrödinger-Benjamin-Ono system) for low-regularityinitial data in both periodic and continuous cases; secondly, a family of newperiodic traveling waves for the Schrödinger-Benjamin-Ono system is given:by fixing a minimal period we obtain, via the implicit function theorem, asmooth branch of periodic solutions bifurcating a Jacobian elliptic functioncalled dnoidal, and, moreover, we prove that all these periodic traveling wavesare nonlinearly stable by perturbations with the same wavelength.