Low Earth orbit (LEO) satellite networks have shown extensive application in the fields of navigation, communication services in remote areas, and disaster early warning. Inspired by multi-access edge computing (MEC) technology, satellite edge computing (SEC) technology emerges, which deploys mobile edge computing on satellites to achieve lower service latency by leveraging the advantage of satellites being closer to users. However, due to the limitations in the size and power of LEO satellites, processing computationally intensive tasks with a single satellite may overload it, reducing its lifespan and resulting in high service latency. In this paper, we consider a scenario of multi-satellite collaborative offloading. We mainly focus on computation offloading in the satellite edge computing network (SECN) by jointly considering the transmission power and task assignment ratios. A maximum delay minimization problem under the power and energy constraints is formulated, and a distributed balance increasing penalty dual decomposition (DB-IPDD) algorithm is proposed, utilizing the triple-layer computing structure that can leverage the computing resources of multiple LEO satellites. Simulation results demonstrate the advantage of the proposed solution over several baseline schemes.