Observation of p orbital magnetism in some compounds with no transition element has opened a new magnetic field. These compounds include some ionic binary alloys such as CaN and CaC. In these two compounds, ferromagnetic behavior is accompanied with half-metallic characteristic, which is promising for Spintronics industry. In this project, density functional - pseudo potential computations were performed to study the structural and magnetic properties of the rocksalt (RS) and zinc-blend (ZB) structures of bulk CaC and CaN and their monolayer and bilayer on Cu (001). We observed that CaN exhibits half-metallic ferromagnetism in both RS and ZB structures, while RS-CaN is more stable and more stiff. The structural properties of RS- and ZB-CaN and CaC monolayers are studied and the relative stability of different interface terminations and patterns were investigated and stable structures were identified.In contrast to the bulk CaN, the induced strain by Cu (001) substrate on CaN thin film effectively enhances stability of the ZB-CaN monolayers. It was argued that the N terminated CaN monolayers on Cu (001) are non or weak magnetic system with considerable lower energy than the Ca terminated monolayers exhibiting half-metallic ferromagnetism. This observation was attributed to the strong Cu-N and Cu-C and weak Cu-Ca bonding at the interface. The climbing image nudged elastic band calculations indicated an activation barrier of about 1.18 eV per CaN unit between the high energy ferromagnetic and the stable nonmagnetic CaN monolayer on Cu (001). Therefore, epitaxial growth of a Ca terminated CaN thin film on Cu (001) is likely a practical way to form a new half-metal/metal junction. The magnetic and electronic properties of different interface terminations of CaN and CaC bilayer on Cu (001) were also studied. It was seen that surface anion layers of the Ca terminated bilayers preserves their half metallic character.