This study employs two-dimensional axisymmetric relativistic magnetohydrodynamic simulations to investigate the evolution of supernova remnant (SNR) and pulsar wind nebula (PWN) composite systems in two distinct interstellar medium (ISM) configurations: a uniform density distribution and a medium with a sharp density discontinuity. Compared to the uniform density distribution, the ISM with this density discontinuity better reflects the actual conditions and explains the overall morphological characteristics of specific types of SNR-PWN composite systems. These systems exhibit asymmetries, such as an SNR shell with differing radii or an inner PWN located nearer to the shell on one side. The simulation results suggest that the density discontinuity in the ISM is a contributing factor to both the shell asymmetry and the PWN displacement. Specifically, this density variation directly causes the inconsistency in the forward shock speeds of the SNR between high and low density regions, resulting in discrepancies in the shell layer radii. Furthermore, the asymmetric morphology of the PWN and its positional offset emerge through interactions with the reverse shock. The PWN tends to shift toward the SNR shell on one side. The greater the density jump in the background field, the more pronounced the shell radius differences and PWN offset become.