In the present work, the effects of blending dimethyl ether (DME) and hydrogen (H2) with methane (CH4) have been numerically studied in the context of counterflow diffusion flames. In order to do so, a reaction mechanism consisting of 974 reaction steps among 146 species with updated thermodynamic and transport properties has been developed. This mechanism has been validated against the experimental data on laminar burning velocity, ignition delay time and species profiles in counterflow diffusion flames. The present study suggests that the heat release pattern of the CH4 counter flow diffusion flame shows major changes when DME and H2 are present in the fuel stream. Furthermore, the results show that the presence of low volume fractions of DME in CH4 increases the formation of benzene (C6H6) in the flame. This fact can be negated by the presence of H2 together with CH4 and DME in the fuel stream. Moreover, the present study suggests that H2 mitigates the C6H6 formation in the CH4 diffusion flame with greater effectiveness compared to DME. Contrary to the popular belief, the main reason behind such efficacy of H2 has been found to be physical rather than chemical. On the other hand, the NO production routes are primarily dominated by the Zeldovich mechanism in the flames involving CH4, DME and H2 blends. In this regard, the present analysis suggests that the simultaneous presence of DME and H2 in CH4 effectively prevents the formation of NO in the flame.