Structural evolution of Cu nanolayer deposited on chemically modified Si substrates has been studied by X-ray reflectivity (XRR), atomic force microscopy (AFM) and scanning electron microscopy (SEM) techniques as a function of time. It is evident from the experimental results that two completely different phenomena, namely dewetting (usually observed for highly abrupt interface system like Ag/Si) and interdiffusion (usually observed for highly diffusive interface system like Au/Si), take place simultaneously or co-exist at the interface of such Cu/Si system and thus can be treated as a model system (showing intermediate of two extreme natures). The dual character of Cu/Si system, however, strongly depends on the chemical species, such as hydrogen and bromine, by which Si surface (dangling bonds) is terminated. For example, the interdiffusion of Cu is found more into the H-terminated Si substrate compared to the Br-terminated one (similar to that of the Au/Si system), while the dewetting is dominant on the Br-terminated Si surface compared to the H-terminated Si (similar to that of the Ag/Si system). Such evolution of growth mainly involves dewetting of Cu on the freshly grown silicon oxide areas on the terminated Si substrate (related to the change in the interfacial energy due to the oxide-growth with time by destroying termination) to change the topography of the Cu nanolayer and also interdiffusion of Cu through the silicon oxide free areas (related to the size and electronegativity differences between Cu and Si) to form a very thin interdiffused layer of Cu into Si.