This paper proposes a proportional fair-based joint optimization method for user association and the bandwidth ratio of protected radio resources exclusively used by pico base stations (BSs) for inter-cell interference coordination (ICIC) in heterogeneous networks where low transmission-power pico BSs overlay a high transmission-power macro BS. The proposed method employs an iterative algorithm, in which the user association process for a given bandwidth ratio of protected radio resources and the bandwidth ratio control of protected radio resources for a given user association are applied alternately and repeatedly up to convergence. For user association, we use our previously reported decentralized iterative user association method based on the feedback information of each individual user assisted by a small amount of broadcast information from the respective BSs. Based on numerical results, we show that the proposed method adaptively achieves optimal user association and bandwidth ratio control of protected radio resources, which maximizes the geometric mean user throughput within the macrocell coverage area. The system throughput of the proposed method is compared to that for conventional approaches to show the performance gain.