Spatial coupling is utilized to improve the performance of iterative channel estimation, multiuser detection, and decoding for multiple-input multiple-input (MIMO) bit-interleaved coded modulation (BICM). Coupling is applied to both coding and BICM---the encoder uses a protograph-based spatially-coupled low-density parity-check (SC LDPC) code. Spatially and temporally coupled (STC) BICM is proposed to enable iterative channel estimation via coupling. Linear minimum mean-squared error (LMMSE) estimation is applied for both channel estimation and detection to reduce the complexity. Tractable density evolution (DE) equations are derived to analyze the convergence property of iterative receivers in the large-system limit, via a tool developed in statistical physics---replica method. The DE analysis implies that the STC BICM can improve the performance of iterative channel estimation especially for higher-order modulation. Numerical simulations show that the STC BICM can provide a significant gain of the performance at high signal-to-noise ratios for 64 quadrature amplitude modulation (QAM), as well as an improvement in the decoding threshold, compared to conventional BICM.