Target detection embedded in a complex interference background such as jamming or strong clutter is an important problem in signal processing. Traditionally, statistical adaptive detection processes are built from a binary hypothesis test performing on a grid of steering vectors. This usually involves the estimation of the noise-plus-interference covariance matrix using i.i.d. samples assumed to be target-free. Moving from this paradigm, we exploit the fact that the interference (clutter and/or jammers) lies in a union of low-dimensional subspaces. Hence, the matrix of concatenated samples can be modeled as a sum of low-rank matrices (union of subspaces containing interferences) plus a sparse matrix times a dictionary of steering-vectors (rep-resenting the targets contribution). Recovering this factorization from the observation matrix allows to build detection maps for each sample. To perform such recovery, we propose a generalized version of the robust subspace recovery via bi-sparsity pursuit algorithm . Experimental results on a real data set highlight the interest of the approach.