In today's era of Internet of Things (IoT), where massive amounts of data are produced by IoT and other devices, edge computing has emerged as a prominent paradigm for low-latency data processing. However, applications may have diverse latency requirements: certain latency-sensitive processing operations may need to be performed at the edge, while delay-tolerant operations can be performed on the cloud, without occupying the potentially limited edge computing resources. To achieve that, we envision an environment where computing resources are distributed across edge and cloud offerings. In this paper, we present the design of CLEDGE (CLoud + EDGE), an information-centric hybrid cloud-edge framework, aiming to maximize the on-time completion of computational tasks offloaded by applications with diverse latency requirements. The design of CLEDGE is motivated by the networking challenges that mixed reality researchers face. Our evaluation demonstrates that CLEDGE can complete on-time more than 90% of offloaded tasks with modest overheads.