We recently proposed REXPACO, an algorithm for imaging circumstellar environments from high-contrast angular differential imaging (ADI) data. In the context of high-contrast imaging where the signal of interest is largely dominated by a nuisance term due to the stellar light leakages and the noise, our algorithm amounts to jointly estimating the object of interest and the statistics (mean and covariance matrix) of the nuisance component. In this contribution, we first extend the REXPACO algorithm by refining the statistical model of the nuisance component it embeds. Capitalizing on the improved robustness of this new method named robust REXPACO, we then show how it can be modified to deal with angular plus spectral differential imaging (ASDI) datasets. We apply our methods on several ADI and ASDI datasets from the IRDIS and IFS imagers of the VLT/SPHERE instrument and we show that the proposed algorithms significantly reduce the typical artifacts produced by stateof-the-art algorithms. By also taking into account the instrumental point spread function (PSF), our algorithms yield a deblurred estimate of the object of interest without the artifacts observed with other methods.