Trellis coded modulation (TCM) is a bandwidth efficient transmission scheme that can achieve high coding gain by integrating coding and modulation. This paper presents an analytical expression for the error event probability of TCM with transmit diversity (Realized by space-time block coding) which reveals some dominant factors affecting the system performance over slow fading channels when perfect interleavers are used. This leads to establishing the design criteria for constructing optimal trellis codes for use with space-time block coding over flat fading channels. These results also apply to fast fading channels where the maximum Doppler spread normalized by the symbol rate is of the order of 10-2. Through simulation, significant performance improvement is shown to be achieved by concatenating the interleaved streams of these codes with space-time block codes over fading channels. Simulation results also demonstrate that these outer codes have better error performance than codes of the same number of states design for Gaussian or fading channels without the use of transmit diversity.