Conservative schemes have been extensively studied in the last few decades for smooth systems of differential equations and reached a certain maturity. In various areas of research in modern science, one encounters many important nonsmooth problems which admit some essential conservative properties. Their existing numerical treatments, to our knowledge, were rarely investigated in appropriate conservative manners. In this talk, we consider a nonsmooth system originated from the nonlinear Schrődinger equations with delta potentials, and propose a kind of numerical schemes which, are elaborately constructed by applying discrete gradient and immersed interface methods to the time and space respectively. With the help of introducing new weight coefficients, we prove that not only the energy but the normalization can be preserved exactly. Based on these conservation properties, we show rigorously the solvability of the schemes and the pointwise boundedness of the numerical solutions. Convergence analysis is then conducted for the schemes and optimal error estimates are obtained. Numerical experiments are presented to verify our theoretical results.