Large language models have been widely deployed in various applications, encompassing both interactive online tasks and batched offline tasks. Given the burstiness and latency sensitivity of online tasks, over-provisioning resources is common practice. This allows for the integration of latency-insensitive offline tasks during periods of low online load, enhancing resource utilization. However, strategically serving online and offline tasks through a preemption mechanism fails to fully leverage the flexibility of offline tasks and suffers from KV cache recomputation and irregular workloads. In this paper, we introduce Echo, a collaborative online-offline task serving system, including a scheduler, a KV cache manager, and estimation toolkits. The scheduler and KV cache manager work tightly to maximize the throughput of offline tasks, while the estimator further predicts execution time to ensure online task SLOs. The scheduler leverages the batch information of last iteration to reduce the search space for finding the optimal schedule. The KV cache manager sets the priority of the KV cache based on the type of tasks and the opportunity of prefix sharing to reduce the recomputation. Finally, the estimation toolkits predict the execution time, future memory consumption, and the throughput of offline tasks to guide the scheduler, KV cache manager, and the system deployer. Evaluation based on real-world workloads demonstrates that Echo can increase offline task throughput by up to $3.3\times$, while satisfying online task SLOs.