The problem of joint resource allocation and relay selection is studied for bidirectional LTE-advanced relay networks. The bidirectional communication between user equipment (UE) and eNodeB (eNB) is performed via direct transmission, co-operative relaying (CoR), or a combination of network coding (NC) and CoR (NC/CoR). In this paper, an enhanced three-time-slot per cycle time-division duplexing (TDD) scheme is proposed for LTE-Advanced frame architecture to accommodate a hybrid transmission scheme. More specifically, we formulate the problem of joint resource assignment, relay selection, and bidirectional transmission scheme selection as a combinatorial optimization problem with the objective to maximize the total product of backlog and rate (back-pressure principle). Two approaches are considered to solve our combinatorial optimization problem. First, a graph-based framework is proposed in which the problem is transformed into a maximum weighted Clique problem (MWCP). In addition, our problem is also transformed into a three-dimensional assignment problem (3DAP) which is solved using a hybrid ant colony optimization (ACO) algorithm. Using simulations, it is concluded that the hybrid transmission scheme outperforms all conventional nonhybrid schemes. Moreover, the simulation results confirm that while the two proposed solutions provide similar results, the ACO algorithm is faster due to its lower complexity.