The ubiquitous Internet of Things (IoTs) devices spawn growing mobile services of applications with computationally-intensive and latency-sensitive features, which increases the data traffic sharply. Driven by container technology, microservice is emerged with flexibility and scalability by decomposing one service into several independent lightweight parts. To improve the quality of service (QoS) and alleviate the burden of the core network, caching microservices at the edge of networks empowered by the mobile edge computing (MEC) paradigm is envisioned as a promising approach. However, considering the stochastic retrieval requests of IoT devices and time-varying network topology, it brings challenges for IoT devices to decide the caching node selection and microservice replacement independently without complete information of dynamic environments. In light of this, a MEC-enabled di stributed cooperative m icroservice ca ching scheme, named DIMA, is proposed in this paper. Specifically, the microservice caching problem is modeled as a Markov decision process (MDP) to optimize the fetching delay and hit ratio. Moreover, a distributed double dueling deep Q-network (D3QN) based algorithm is proposed, by integrating double DQN and dueling DQN, to solve the formulated MDP, where each IoT device performs actions independently in a decentralized mode. Finally, extensive experimental results are demonstrated that the DIMA is well-performed and more effective than existing baseline schemes.