A two-tier cooperative computing system is considered in this article, where tier-1 consists of multiple mobile edge computing (MEC) servers and tier-2 consists of one mobile cloud computing (MCC) server. We assume that multiple mobile devices (MDs) are allowed to offload their tasks to the MEC and MCC servers. To facilitate task execution for the MDs, both types of servers are deployed with convolutional neural networks (CNNs). We assume that the cooperation between the MEC servers and the MCC server in task execution is enabled by scheduling different layers of the CNNs. To achieve efficient information interaction and task management, we first design a joint task management architecture. Stressing the importance of task execution latency, we formulate the joint task offloading, CNN layer scheduling and resource allocation optimization problem as an overall task latency minimization problem. To solve the formulated optimization problem, we transform it to three subproblems, i.e., CNN layer scheduling subproblem, task offloading subproblem and resource allocation subproblem, and solve the subproblems, respectively, by means of the extensive search algorithm, reformulation-linearization-technique and Lagrange dual algorithm. The effectiveness of the proposed algorithm is demonstrated via numerical simulations.