Dual-connectivity technology enables a base station to assign multiple carriers from various bands to a mobile station (MS), thus increasing its bandwidth and data rate. However, when the downlink frequency assigned to the MS is approximately twice its uplink frequency, the MS's receiver will be seriously interfered by the nonlinear self-interference from its own transmitter. This paper addresses the problem of nonlinear self-interference cancelation for MSs operating in the dual-connectivity mode. Compared with conventional systems, this scenario faces some new challenges because of the wide variety of nonlinear interference components, including not only harmonics but also intermodulation products, and the more complicated interference channels, including both nonlinear and linear devices. In addition, the frequency, bandwidth and frequency-selective channel parameters of the interference are influenced by the uplink resource block allocation. To solve these problems, a two-part nonlinear self-interference canceler is proposed, where one part is designed as a neural network to capture the nonlinear characteristics, and the other part is designed as a linear filter to capture the linear characteristics. Furthermore, a low-complexity two-step training scheme is proposed to approximate the interference channel in the entire system bandwidth. Finally, a hardware prototype is implemented to verify the effectiveness of the proposed scheme. The experimental results show that the proposed scheme achieves more than 20 dB interference cancelation, and significantly outperforms the conventional polynomial-based and pure neural-network cancelation schemes.