In this paper, we generalize a source generative model in a state-of-the-art blind source separation (BSS), independent low-rank matrix analysis (ILRMA). ILRMA is a unified method of frequency-domain independent component analysis and nonnegative matrix factorization and can provide better performance for audio BSS tasks. To further improve the performance and stability of the separation, we introduce an isotropic complex Student's $t$-distribution as a source generative model, which includes the isotropic complex Gaussian distribution used in conventional ILRMA. Experiments are conducted using both music and speech BSS tasks, and the results show the validity of the proposed method.