In this era of Internet of Things (IoT), most of the contemporary researches provide a new dimension of cooperation called Control Channel cooperation to eliminate hidden terminal problem, as well as deafness problem while using directional antenna in a multichannel environment for wireless networks. However, only using such concept of cooperation may increase the communication latency for iterative control channel negotiation. Therefore, cooperation may not only use in information sharing, can be used for relaying data frame to improve throughput and minimize the data transmission delay. In this paper, we have proposed a Two-Dimensional Cooperation-based Asynchronous Multichannel Directional MAC protocol (2D-CMD MAC) that combines both of these cooperation and multi-channel directional concepts of cooperation. This joint concept of cooperation solves the multichannel directional hidden terminal and deafness problems using cooperative information sharing. In addition, cooperation for relaying data in data channel increases the throughput by minimizing the data transmission delay and enhances the channel bandwidth utilization by obtaining parallel transmission in the same data channel. The simulation results show that 2D-CMD MAC improves the network performance in terms of throughput obtained from cooperative data transmission and parallel transmission in same data channel and packet delivery ratio.