Integrated electricity and heat systems facilitate efficient interactions between individual energy sectors for higher renewable energy accommodation. However, the feasibility of operational strategies is difficult to guarantee due to the presence of substantial uncertainties pertinent to renewable energy and multi-energy loads. This paper proposes a novel efficient robust scheduling model of integrated electricity and heat systems based on extensions of disturbance invariant sets. The approach has high computational efficiency and provides flexible and robust strategies with an adjustable level of conservativeness. In particular, the proposed robust scheduling method obtains scheduling strategies by solving a nominal uncertainty-free scheduling problem, whose complexity is identical to a deterministic problem. The robustness against uncertainties is enhanced by endowing the nominal scheduling model with properly tightened constraints considering time-variant uncertainty sets. Towards this end, a novel direct constraint tightening algorithm is developed based on the dual norm to calculate multi-period tightened constraints efficiently without linear programming iterations. Furthermore, the budget uncertainty set is newly combined with constraint tightening to flexibly adjust the conservativeness level of robust solutions. The effectiveness of the proposed robust method is demonstrated in simulation studies of two test systems in terms of computational efficiency, decision robustness and cost reduction.