We measure the elastic and dissipative responses of a multi‐contact interface, formed between the rough surfaces of two contacting macroscopic solids, submitted to a biased oscillating shear force. We evidence that, beyond a linear viscoelastic regime, observed at low shear amplitude, the interface response exhibits a dissipative component that corresponds to the onset of frictional dissipation. The latter regime exists, whereas the tangential force applied, far from the nominal static threshold, does not provoke any sliding. This result, akin to that of Mindlin for a single contact, leads us to extend his model of ‘microslip’ to the case of an interface composed of multiple microcontacts. While describing satisfactorily the elastic response, the model fails to account quantitatively for the observed energy dissipation, which, we believe, results from the fact that the key assumption of local Coulomb friction in Mindlin's model is not legitimate at the sub‐micrometre scale of the microslip zones within microcontacts between surface asperities.