In this paper, we propose a semi-federated learning (SemiFL) framework that allows computing-limited clients to collaboratively train a shared model with resource-abundant clients. Specifically, by supporting the coexistence of model-updating and data-offloading, the SemiFL framework enables both centralized and federated learning in a hybrid fashion. Due to the decoding error, we consider the practical case with residual interference. To improve uplink throughput for centralized learning while reducing aggregation distortion for federated learning, we formulate a non-convex optimization problem to jointly optimize the transmit power and receive strategy. Then, we propose an efficient algorithm to solve the challenging problem by using successive convex approximation. Simulation results demonstrate the effectiveness of our SemiFL framework for heterogeneous networks, and reveal the impact of imperfect signal decoding on communication rates.