Target assignment and path planning are crucial for the cooperativity of multiple unmanned aerial vehicles (UAV) systems. However, it is a challenge considering the dynamics of environments and the partial observability of UAVs. In this article, the problem of multi-UAV target assignment and path planning is formulated as a partially observable Markov decision process (POMDP), and a novel deep reinforcement learning (DRL)-based algorithm is proposed to address it. Specifically, a target assignment network is introduced into the twin-delayed deep deterministic policy gradient (TD3) algorithm to solve the target assignment problem and path planning problem simultaneously. The target assignment network executes target assignment for each step of UAVs, while the TD3 guides UAVs to plan paths for this step based on the assignment result and provides training labels for the optimization of the target assignment network. Experimental results demonstrate that the proposed approach can ensure an optimal complete target allocation and achieve a collision-free path for each UAV in three-dimensional (3D) dynamic multiple-obstacle environments, and present a superior performance in target completion and a better adaptability to complex environments compared with existing methods.