  Two-Way Relay Channel (TWRC) plays an important role in relay networks, and
efficient relaying protocols are particularly important for this model.
{\color{black} However, existing protocols may not be able to realize the
potential of TWRC if the two independent fading channels are not carefully
handled}. In this paper, a Hybrid DeModulate-Forward (HDMF) protocol is
proposed to address such a problem. {\color{black} We first introduce the two
basic components of HDMF - direct and differential DMF, and then propose the
key decision criterion for HDMF based on the corresponding log-likelihood
ratios. We further enhance the protocol so that it can be applied independently
from the modulation schemes. Through extensive mathematical analysis,
theoretical performance of the proposed protocol is investigated. By comparing
with existing protocols, the proposed HDMF has lower error rate. A novel
scheduling scheme for the proposed protocol is introduced, which has lower
length than the benchmark method. The results also reveal the protocol's
potential to improve spectrum efficiency of relay channels with unbalanced
bilateral traffic.}
