Identifying switched linear models directly from input-output measurements only is known to be a non-trivial identification problem. When switched state-space models are considered in a general setting and both the continuous state and the discrete mode are unmeasured, the problem proves to be a much harder realization problem. The present paper describes a method for identifying discrete-time switched linear state-space models from input-state-output measurements. While the discrete mode is unknown, we assume here that the continuous state is measured along with the input and output signals. Given a finite collection of such measured data, we propose a sparsity-inducing optimization approach for estimating the matrices associated with each submodel.