This paper presents a downlink interference mitigation framework for two-tier heterogeneous networks, that consist of spectrum-sharing macrocells and femtocells^*. This framework establishes cooperation between the two tiers through two algorithms, namely, the restricted waterfilling (RWF) algorithm and iterative reweighted least squares interference alignment (IRLS-IA) algorithm. The proposed framework models the macrocell-femtocell two-tier cellular system as an overlay cognitive radio system in which the macrocell system plays the role of the primary user (PU) while the femtocell networks play the role of the cognitive secondary users (SUs). Through the RWF algorithm, the macrocell basestation (MBS) cooperates with the femtocell basestations (FBSs) by releasing some of its eigenmodes to the FBSs to do their transmissions even if the traffic is heavy and the MBS's signal to noise power ratio (SNR) is high. Then, the FBSs are expected to achieve a near optimum sum rate through employing the IRLS-IA algorithm to mitigate both the co-tier and cross-tier interference at the femtocell users' (FUs) receivers. Simulation results show that the proposed IRLS-IA approach provides an improved sum rate for the femtocell users compared to the conventional IA techniques, such as the leakage minimization approach and the nuclear norm based rank constraint rank minimization approach. Additionally, the proposed framework involving both IRLS-IA and RWF algorithms provides an improved total system sum rate compared with the legacy approaches for the case of multiple femtocell networks.