We consider estimation of the multicomponent stress-strength reliability for a general class of inverted exponentiated distributions under progressive type-II censoring. We assume that both stress and strength variables follow this general class of distributions with a common parameter. Different point and interval estimates for the reliability of this system are obtained by using maximum likelihood and Bayesian approaches when the common parameter is known and unknown. The uniformly minimum variance unbiased estimate and exact Bayes estimate under the squared error loss function are derived when the common parameter is known. Bayes estimates are also obtained by using Lindley, Tierney-Kadane and Markov chain Monte Carlo methods. The asymptotic confidence and highest posterior density credible intervals are constructed. Proposed methods are compared numerically using Monte Carlo simulations. Finally, a progressively censored real data set is analyzed for illustration purposes.