Summary: When data generating mechanism generates two correlated data sets both defined on the unit interval, a bivariate probabilistic distribution defined on the unit square is needed for modelling the data. For this purpose, we give a Marshall-Olkin type bivariate extension of an omega distribution in this paper. This is in fact a bivariate unit-exponentiated-half-logistic distribution. We study its mathematical properties in detail. The distribution contains neither an exponential term nor any special function which complicates the computations. Maximum likelihood estimation method and its large sample inference are considered for model parameters. Alternatively, we also propose an expectation-maximization algorithm to compute the estimates. To see the performances of the proposed estimators and validate the theoretical results obtained for estimation, we present the results of a simulation study. Data fitting demonstrations show its applicability in modelling random proportions.