Heterogeneous wireless networks where several systems with different bands coexist for multimedia service are currently in service and will be widely adopted to support various traffic demand. Under heterogeneous networks, a mobile station can transmit over multiple and simultaneous radio access technologies (RATs) such as WLAN, HSPA, and WCDMA LTE. Also, cognitive radio for the efficient use of underutilized/unused frequency band is successfully implemented in some networks. In this letter, we address such operational issues as air interface and band selection for a mobile and power allocation to the chosen links. An optimal solution is sought and analyzed and a distributed joint allocation algorithm is proposed to maximize total system capacity. We investigate the benefit of multiple transmissions by multiple RATs over a single transmission by a single RAT at a time, which can be interpreted as network diversity. Numerical results validate the performance enhancement of our proposed algorithm.