With the aid of blanking nonlinearity, the low density parity check (LDPC) coded bit-interleaved coded modulation (BICM) has been jointly considered as a robust mitigation for the impulsive interference in orthogonal frequency division multiplexing (OFDM) systems. However, the Gaussian assumption for the nonlinear channel conditional probability induces the mismatched L-values in the conventional MAP demodulator. In this paper, combined with the pulse blanking optimization via the PEXIT analysis, we propose a novel MAP demodulator based on the Gaussian mixture model (GMM) and estimate the parameters with the expectation-maximization (EM) algorithm. Taking the L-band Digital Aeronautical Communication System Type1 (L-DACS1) as an example, the GMM-based MAP demodulator can obtain the PEXIT thresholds that match the decoding curves well and provide the better BER performance in the interference-limit channel environment.