We present numerical simulations of symmetric surface-directed spinodal decomposition in thin films with varying film thickness and film composition. The simulations utilize a Cahn-Hilliard model to describe phase separation kinetics in confined film geometries. The systems consist of two phases: a wetting phase that completely wets the top and bottom surfaces, and a nonwetting phase. Three distinct morphologies emerge including a discrete nonwetting morphology, a discrete wetting morphology, as well as a unique two-dimensional bicontinuous morphology that forms for specific values of film thickness and composition. The morphologies are analyzed with a Hoshen-Kopelman algorithm to quantify the degree of continuity of the nonwetting phase, and a morphology map is presented to guide future work.