In this paper, we consider the OFDM-based heterogeneous cognitive radio networks (HCRNs) and investigate the resource allocation problem for heterogenous users which include both Single-network and Multi-homing users in HCRNs with imperfect spectrum sensing and guaranteed quality of service (QoS). In order to maximize the capacity of the OFDM-based HCRNs, the joint subcarrier and power allocation problem is formulated with the total transmission power constraint, interference constraint and QoS constraint. To solve the mixed-inter nonlinear programming problem, it is relaxed to a linear programming problem firstly, and then a suboptimal algorithm with subcarrier assignment and power allocation is proposed based on the relaxed optimal solution. Simulation results are presented to demonstrate that the improved capacity of HCRNs can be obtained by the proposed algorithm. Besides, the communication of the primary users in HCRNs can be protected by taking sensing errors into consideration.