Ambient backscatter communication (AmBC) leverages the existing ambient radio frequency (RF) environment to implement communication with battery-free devices. The key challenge in the development of AmBC is the very weak RF signals backscattered by the AmBC Tag. To overcome this challenge, we propose the use of orthogonal space-time block codes (OSTBC) by incorporating multiple antennas at the Tag as well as at the Reader. Our approach considers both coherent and non-coherent OSTBC so that systems with and without channel state information can be considered. To allow the application of OSTBC, we develop an approximate linearized and normalized multiple-input multiple-output (MIMO) channel model for the AmBC system. This MIMO channel model is shown to be accurate for a wide range of useful operating conditions. Two coherent detectors and a non-coherent detector are also provided based on the proposed AmBC channel model. Simulation results show that enhanced bit error rate performance can be achieved, demonstrating the benefit of using multiple antennas at the Tag as well as the Reader.