Video quality assessment is essential for the performance analysis of visual communication applications. Objective metrics can be used for estimating the relative quality differences, but they typically give reliable results only if the compared videos contain similar types of quality distortion. However, video compression typically produces different kinds of visual artifacts than transmission errors. In this article, we focus on a novel subjective quality assessment method that is suitable for comparing different types of quality distortions. The proposed method has been used to evaluate how well different objective quality metrics estimate the relative subjective quality levels for content with different types of quality distortions. Our conclusion is that none of the studied objective metrics works reliably for assessing the co-impact of compression artifacts and transmission errors on the subjective quality. Nevertheless, we have observed that the objective metrics' tendency to either over-or underestimate the perceived impact of transmission errors has a high correlation with the spatial and temporal activity levels of the content. Therefore, our results can be useful for improving the performance of objective metrics in the presence of both source and channel distortions.