With the popularization of the cloud-edge collaborative environment, the optimization of container scheduling has become a crucial challenge for enhancing system performance. Existing methods often overlook the sharing property of image layers and the load balancing among multiple clusters, resulting in high container startup latency and low resource utilization. To tackle this problem, a Layer-sharing Container Scheduling (LSCS) scheme is put forward in this paper. This scheme consists of two algorithms: Probabilistic Relaxation Container Scheduling (PRCS) and Greedy Layer Sorting (GLS). PRCS achieves load balancing while satisfying resource constraints through linear programming relaxation and random rounding techniques. GLS transforms the layer download order problem into a single-machine scheduling problem and utilizes the Sidney decomposition algorithm to optimize the startup latency. Experiments show that LSCS reduces the container startup latency by approximately 30\% compared with the baseline algorithms, and optimizes the load balancing by about 39\% compared with the baseline algorithms.