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In this paper, the exponential stability is considered for a class of switched systems containing both stable and unstable subsystems with impulsive effect by using the matrix measure concept and average dwell time approach. The authors show that if the average dwell time and the ratio of the total activation time (of those subsystems) with negative matrix measure to the total activation time (of those subsystems) with nonnegative matrix measure are both chosen appropriately large, the exponential stability of a desired degree is guaranteed. Under a similar condition, the robust exponential stability problem for a class of switched systems with impulsive effect and structure perturbations is also studied. Simulations validate the main results.