Capacity scaling of a large hybrid network with unit node density, consisting of $n$ wireless ad hoc nodes, base stations (BSs) equipped with multiple antennas, and one remote central processor (RCP), is analyzed when wired backhaul links between the BSs and the RCP are rate-limited. We deal with a general scenario where the number of BSs, the number of antennas at each BS, and the backhaul link rate can scale at arbitrary rates relative to $n$ (i.e., we introduce three scaling parameters). We first derive the minimum backhaul link rate required to achieve the same capacity scaling law as in the infinite-capacity backhaul link case. Assuming an arbitrary rate scaling of each backhaul link, a generalized achievable throughput scaling law is then analyzed in the network based on using one of pure multihop, hierarchical cooperation, and two infrastructure-supported routing protocols, and moreover, three-dimensional information-theoretic operating regimes are explicitly identified according to the three scaling parameters. In particular, we show the case where our network having a power limitation is also fundamentally in the degrees-of-freedom- or infrastructure-limited regime, or both. In addition, a generalized cut-set upper bound under the network model is derived by cutting not only the wireless connections but also the wired connections. It is shown that our upper bound matches the achievable throughput scaling even under realistic network conditions such that each backhaul link rate scales slower than the aforementioned minimum-required backhaul link rate.