To address the novel space-near space-air based cooperative earth observation (SNA-EO) with coverage, monitoring, and tracking requirements, this paper studies the planning models and the algorithm for three typical SNA-EO missions. Firstly, a general routing decision model is built to describe the observation routes of different SNA-EO resources. Then, a differentiated constraint and objective model is given to formulize the SNA-EO missions, including regional target coverage, fixed target monitoring, and moving target tracking. Also, the coverage rate, monitoring rate, and tracking rate are defined as objective functions of these three missions, respectively. To solve the models in a flexible, easy-to-use, and self-adaptive manner, a parallel competing memetic algorithm that makes full use of inner algorithms and operators via parallel, competing, and evolutionary strategies is proposed. The models and the algorithm are experimentally examined in cases of the three SNA-EO missions, where the SNA-EO cooperation in space and time domain is properly presented. Finally, the feasibility and suggestions of the models and the algorithm in real-world applications are discussed.