In this paper we propose a new robust identification framework that combines both frequency and time-domain experimental data. The main result of the paper shows that the problem of obtaining a nominal model consistent with the experimental data and bounds on the identification error can be recast as a constrained finite-dimensional convex optimization problem that can be efficiently solved using Linear Matrix Inequalities techniques. This approach, based upon a generalized interpolation theory, contains as special cases the Caratheodory-Fejer (purely time-domain) and Nevanlinna-Pick (purely frequency-domain) problems. The proposed procedure interpolates the frequency and time domain experimental data while restricting the identified system to be in an a priori given class of models, resulting in a nominal model consistent with both sources of data. Thus, it is convergent and optimal up to a factor of two (with respect to central algorithms).