Overlay multicasting providing live streaming services became crucial service in contemporary Internet. In this paper, we focus on applying the overlay multicasting for delivering of critical data that require to be transmitted safely, intact and with as little delay as possible. To improve survivability of the overlay multicasting, we propose to use dual homing approach, i.e., each peer is connected to the overlay by two separate access links. We consider the following network failures: overlay link failure, uploading node failure and ISP interconnection failure. The main goal of our experiments is to determine the additional cost of providing survivability to the overlay multicasting network with dual homing technology for both flow assignment and capacity and flow assignment problems. Our studies indicate that the additional survivability requirements do not have a substantial impact on the overlay multicasting system expressed as streaming cost or network cost.