This paper deals with the problem of output regulation for a class of hybrid linear SISO systems and exosystems whose dynamics have jumps according to the value of a clock variable. The problem of designing controllers embedding an hybrid internal model of the switching exosystem in order to achieve the regulation objective is addressed. Key concepts and tools well known in the field of output regulation for continuous-time systems, such as the concept of steady-state response, of regulator equations and the internal model property, are thus generalized to the hybrid setting. Emphasis is placed on internal models and stabilizers that are robust to uncertainties entering both in the flow and jump dynamics of the hybrid controlled system. Time-varying and time-independent design principles are presented. Simulation results show the effectiveness of the proposed solutions in meaningful cases.