In this paper, we develop a general framework to analyze the rate performance of a two-tier MIMO heterogeneous network (HetNet) with wireless backhaul under spatial multiplexing. We consider linear precoding and receive filtering in the presence of interference from uplink and downlink transmissions. We find that the sum rate per area of the HetNet is sensitive to the network load, i.e., the number of users served by each base station. We show that a two-tier HetNet with wireless backhaul can achieve higher sum rate per area than a one-tier cellular network. However, this requires the bandwidth division between radio access links and wireless backhaul to be optimally designed according to the load conditions.