In this paper, we consider multi-homing in terms of the emerging long-term evolution in unlicensed band (LTE-U) technology. Accordingly, the unlicensed band can be simultaneously and dynamically shared by every single user between the two radio access technologies (RATs), WiFi and LTE-U, to boost the system performance and enhance the user experience as well. Because of the additive freedom on unlicensed band, the problem of multi-RAT selection and resource allocation is much more complicated. To realize multi-homing in LTE-U networks, we aim at maximizing the overall throughput of multi-homing users while guaranteeing the quality of service and the power limitation. First, the sufficient conditions for each user to select only one RAT for transmission are developed. Then, since the multi-RAT selection and resource allocation problem is NP-hard, an effective heuristic algorithm is proposed to solve it. Numerical results validate the effectiveness of our proposed algorithm and demonstrate that the proposed mechanism can enhance the system throughput compared with traditional single-homing LTE-U networks.