Following the proliferation of three-dimensional video contents and displays, many terrestrial broadcasting companies have been preparing for stereoscopic 3DTV service. In terrestrial stereoscopic broadcast, it is a difficult task to code and transmit two video sequences while sustaining as high quality as 2DTV broadcast due to the limited bandwidth defined by the existing digital TV standards such as ATSC. Thus, a terrestrial 3DTV broadcasting with a heterogeneous video codec system, where the left image and right images are based on MPEG-2 and H.264/AVC, respectively, is considered in order to achieve both high quality broadcasting service and compatibility for the existing 2DTV viewers. Without significant change in the current terrestrial broadcasting systems, we propose a joint rate control scheme for stereoscopic 3DTV service based on the heterogeneous dual codec systems. The proposed joint rate control scheme applies to the MPEG-2 encoder a quadratic rate-quantization model which is adopted in the H.264/AVC. Then the controller is designed for the sum of the left and right bitstreams to meet the bandwidth requirement of broadcasting standards while the sum of image distortions is minimized by adjusting quantization parameter obtained from the proposed optimization scheme. Besides, we consider a condition on maintaining quality difference between the left and right images around a desired level in the optimization in order to mitigate negative effects on human visual system. Experimental results demonstrate that the proposed bit rate control scheme outperforms the rate control method where each video coding standard uses its own bit rate control algorithm independently in terms of the increase in PSNR by 2.02%, the decrease in the average absolute quality difference by 77.6% and the reduction in the variance of the quality difference by 74.38%.