Efficient utilization of limited spectrum resource has been a major issue in wireless communication systems, which has triggered the design and development of advanced cellular networks. Recently, heterogeneous network (HetNet) with small cells to satisfy the demand for higher data rate transmission and throughput has attracted a lot of attention in the unlicensed spectrum bands environment to overcome the scarcity of licensed spectrum. In this paper, we consider network capacity optimization problem for HetNet comprised of Long-Term Evolution (LTE) small cell and wireless fidelity (Wi-Fi) in LTE unlicensed spectrum (LTE-U) with optimal spectrum splitting ratio. We derive coverage probabilities and average achievable rates for each radio access technologies (RATs) based on the conditions of user equipment (UE) association in multi-RAT wireless network system. Then the optimal unlicensed spectrum splitting ratio can be obtained by maximizing HetNet capacity under the derived constraints on respective coverage probabilities. Simulation results reveal effectiveness of the proposed scheme, where both the spectrum splitting ratio and transmit power ratio are key parameters. This analysis can be easily extended to HetNets with multiple RATs.