Recently, the use of heterogeneous small-cell networks to offload traffic from existing cellular systems has attracted considerable attention. One of the significant challenges in heterogeneous networks (HetNet) is cross-tier interference, which becomes significant when macro-cell users (MUE) are in the vicinity of femtocell base stations (FBS). Indeed, the femtocell will cause significant interference to MUEs on the macrocell downlink (DL) while MUEs will induce hefty interference to the femtocell on the macrocell uplink (UL). Substantial work has focused on offloading and interference mitigation in HetNets; yet, none of them has considered the impact of cross-tier interference on quality of service (QoS), quality of experience (QoE). This paper proposes the Quality Efficient Femtocell Offloading Scheme (QEFOS) that selects the users most affected by the interference encountered and offloads them to nearby FBSs. QEFOS testing shows substantial improvements in terms of QoS and QoE perceived by users in heavy cross-tier interference scenarios in comparison with alternative approaches. In particular QEFOS's impact on throughput, packet loss ratio (PLR), peak-to-signalnoise ratio (PSNR), and structural similarity identity matrix (SSIM) was assessed.