Hybrid broadcast networks are particularly envisaged to merge broadcast TV with broadband Internet and to act as a key enabler for new and better video services in the near future. This is expected to contribute for the evolution of 3-D and multiview video services due to the inherent diversity of its coded data, comprising several complementary streams. Using the multiview video-plus-depth format, at least two independent streams may be delivered through different channels over a hybrid network, that is, broadcasting backward compatible 2-D video in one channel and delivering its corresponding depth stream through complementary channels like LTE-based broadband Internet accesses. This article addresses the problem of monitoring the quality of 3-D video (color plus depth) delivered in such hybrid networking environments, proposing a novel scheme to estimate the impact of visual quality degradation resulting from packet losses in the broadband Internet carrying only the depth stream, without relying on the texture component of the video or any other reference data. A novel non-reference (NR) approach is described, operating as a cascade of two estimators, using only header information of the packets carrying the depth stream through IP broadband. The two-stage cascaded estimator comprises an NR packet-layer model based on an artificial neural network followed by a logistic model, with each stage outputting a separate quality estimate. Performance evaluations, done by comparing the actual and estimated scores for the structural similarity index and subjective differential mean-opinion score, reveals high accuracy for both of these estimates, with Pearson linear correlation coefficient values greater than 0.89. Since only packet-layer information is used, the algorithmic complexity of this monitoring tool is low, making it suitable for standalone implementation at arbitrary network nodes.