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We develop a unified framework for the performance analysis of arbitrary-loaded downlink heterogeneous networks (HetNets) in which interfering sources are inherently spatially-correlated. Considering a randomly-deployed multi-tier cellular network comprised of a diverse set of large-and small-cells, we incorporate the notion of load-awareness and spatial-correlations in characterizing the activities of base stations (BSs) using binary decision variables. A stochastic geometry-based approach is accordingly employed to systematically develop a bounded expression of ergodic rate with different cellular association and load-balancing strategies. Employing the proposed unified framework hence allows for relaxation of several major limitations in the existing state-of-the-art models, in particular the always-transmitting-BSs, uncorrelated interferers, and Rayleigh fading assumptions. We elaborate on the usefulness of adopting this methodology by providing detailed analysis of the aggregate network interference generated by interdependent load-proportional sources over Nakagami-m fading interfering channels. The analytical formulations are validated through Monte-Carlo (MC) simulations for various scenarios and system settings of interest. We observe that the heavily-adopted fully-loaded model as well as the more recent interference-thinning-based approximations are significantly limited in capturing the actual performance curve. The proposed bounded load-aware model and MC trials reveal several important trends and design guidelines for the practical deployment of HetNets. [ABSTRACT FROM PUBLISHER]