We study a general type of multiple-input multiple-output (G-MIMO) relay channels, which consist of two groups (A and B) of source nodes and one relay node. Both groups have arbitrarily many source nodes each of which is in turn equipped with an arbitrary number of antennas. A G-MIMO relay channel engages in two-way transmission of independent information via the relay node. We obtain a tight upper bound on the total degrees of freedom (DoF) for such G-MIMO relay channels. Under the reasonable assumption that the number of antennas at the relay node is no more than the total number of antennas of either Group A or B, we design an efficient transmission scheme to achieve the upper bound by using techniques of signal alignment and joint transceiver design for interference cancellation. At the end of the paper, we propose a future research topic to quantify the relationship between graded levels of network security and the corresponding DoF of the G-MIMO relay channels.