The archetypal metal-organic framework-5 (MOF-5 or IRMOF-1) has been explored as a benchmark sorbent material with untapped potential to be studied in the capture and storage of gases and chemical confinement. Several derivatives of this framework have been prepared using the multivariate (MTV) strategy through mixing size-matching linkers to isolate, for example, MIXMOFs that outperform same-linker congeners when employed as gas reservoirs. Herein, we describe a straightforward protocol that uses mechanosynthesis (solvent-free grinding) followed by mild activation in dimethylformamide (DMF)/CHCl3 (40 °C and ambient pressure) to synthesize a functional phase-pure interpenetrated MOF-5 (int-MOF-5) bearing the size-matching 1,4-benzene dicarboxylate (BDC) and 1,2,4,5-tetrazine-3,6-dicarboxylate (TZDC) linkers in the backbone of the interpenetrated MIXMOF. We found that the grinding involving a mixture of H2TZDC and H2BDC in a 1:4 ratio (20% of H2TZDC) in the presence of zinc(II) acetate yields a crystalline solid that upon activation forms a phase-pure int-MOF-5 herein referred to as 20%TZDC-MOF-5. The crystalline phase, thermal stability, and porous structure of 20%TZDC-MOF-5 were thoroughly characterized, and the gas adsorption performance of the MIXMOF was investigated through the isotherms of N2 and H2 at 77 K and CO2 at 273 and 296 K. The pore size distribution for 20%TZDC-MOF-5 was found to be very similar to that determined using single crystals of the same-linker int-MOF-5. The presence of TZDC in the MIXMOF led to a slight increase in the uptake values for both H2 and CO2, suggesting that beneficial interactions take place. To the best of our knowledge, this is the first report presenting a suitable protocol to yield a functionalized int-MOF-5 as a promising means of synergistically fine-tuning the confinement of small target molecules such as CO2 and H2.