We develop a comprehensive analytical model for multiple long-lived multipath Transmission Control Protocol (TCP) connections downloading content from a remote server in the Internet using parallel paths with Wi-Fi and cellular last-miles. This is the first analytical model developed in the literature that captures the coupling between the paths through heterogeneous wireless networks where the coupling arises due to the multipath TCP coupled congestion control protocol. The model also takes into account the impact of the shared nature of the wireless medium and the finite access point (AP) buffer in the Wi-Fi last-mile. The accuracy of the proposed model is demonstrated via extensive ns-2 simulations. Furthermore, we discover a new type of throughput unfairness among the competing regular and multipath TCP connections going through the same AP with a droptail buffer; the regular TCP connections essentially steal almost all the Wi-Fi bandwidth away from the multipath TCP connections. To tackle this problem, we present two simple solutions utilizing our analytical model and achieve fairness.