Densifying the cellular networks has been largely considered as a promising solution in meeting the capacity demands of emerging cellular networks that have expeditiously transformed from voice-oriented to data-oriented. However, densifying the network infrastructure is like a double-edged sword; it on one hand helps in achieving the desired data rates but on the other hand, it degrades the network coverage. Owing to the disparity in transmit power of macro base stations (MBSs) and small BSs (SBSs), the SBSs located in the close proximity of MBSs have negligible coverage areas that not only overburden the macro tier but also cause excessive interference. In order to overcome these limitations, we propose to mute the SBSs that are located in the near-vicinity of MBSs to introduce a partial-correlation between the locations of the BS tiers. Meanwhile, to further enhance the coverage performance of these coverage-centric cellular networks, the traditional load balancing mechanism along with interference abating strategy is also employed in this paper. Nonetheless, it is also well-known in the literature that the usage of single-slope path loss model (PLM) leads to significant inaccuracies in evaluating the performance of dense cellular networks. Therefore, a more accurate PLM based on the dual-slope is adopted in this paper. Analytical expressions for the tier association and coverage probability are derived for a randomly chosen user using the tools from stochastic geometry and validated through simulations. The numerical results testify the improvement in network coverage due to the non-uniform deployment of SBSs and the joint consideration of load balancing and interference mitigation mechanisms.