Content-centric mobile hybrid Internet-of-Things (IoT) networks consisting of mobile devices and static femto access points (FAPs) are studied, where each device moves according to the random walk mobility model and requests a content object from the library independently at random according to a Zipf popularity distribution. Instead of allowing access to content objects at macro base stations via costly backhaul providing connection to the core network, we consider a more practical scenario where mobile devices and static FAPs, each having a finite-size cache space, are able to cache a subset of content objects so that each request is served by other mobile devices or static FAPs. Under a general multihop-based content delivery protocol, we analyze the order-optimal throughput--delay trade-off by presenting a new cache allocation strategy. In particular, under a given caching strategy, we first characterize a throughput--delay trade-off in terms of scaling laws along with the general content delivery multihop routing protocol. Then, the order-optimal throughput--delay trade-off is characterized by presenting the order-optimal cache allocation strategy, which jointly finds the replication sets at mobile devices and static FAPs via a novel variable decoupling approach. In our mobile IoT network, an interesting observation is that highly popular content objects are mainly served by mobile devices while the rest of content objects are served by static FAPs. We perform numerical evaluation to validate our analytical results. We also show that the order-optimal strategy strictly outperforms a baseline approach, where the replication sets at mobile devices and static FAPs are optimized separately.