This study investigates the applications of reconfigurable intelligent surfaces (RIS) in heterogeneous downlink networks (HetNet). Due to the network densification, the small cell base station (SBS) interferes with the macrocell users (MUE). In this paper, we utilize RIS to mitigate cross-tier interference in an HetNet via directional beamforming by adjusting the phase shift of the RIS. We consider an RIS-assisted HetNet consisting of multiple SBS nodes and MUEs that utilize both direct paths and reflected paths. Therefore, the aim of this study is to maximize the sum rate of all MUEs by jointly optimizing the transmit beamforming of the macrocell base station (MBS) and the phase shift of the RIS. An efficient RIS reflecting coefficients-based optimization (RCO) is proposed based on a successive convex approximation approach. Simulation results are provided to show the effectiveness of the proposed scheme in terms of its sum rate in comparison with the scheme HetNet without RIS and the scheme HetNet with RIS but with random phase shifts.