The optimization of joint source and channel coding for a sequence of numerous progressive packets is a challenging problem. Further, the problem becomes more complicated if the space-time coding is also involved with the optimization in a multiple-input multiple-output (MIMO) system. This is because the number of ways of jointly assigning channels codes and space-time codes to progressive packets is much larger than that of solely assigning channel codes to the packets. We are unaware of any feasible and complete solution for such optimization of joint source, channel, and space-time coding of progressive packets. This paper applies a parametric approach to address that complex joint optimization problem in a MIMO system. We use the parametric methodology to derive some useful theoretical results, and then exploit those results to propose an optimization method where the joint assignment of channel codes and space-time codes to the packets can be optimized in a packet-by-packet manner. As a result, the computational complexity of the optimization is exponentially reduced, compared to the conventional exhaustive search. The numerical results show that the proposed method significantly improves the peak-signal-to-noise ratio performance of the rate-based optimal solution in a MIMO system.