Four two-dimensional (2D), fluorinated metal-organic frameworks (MOFs), [Cu(hfipbb)(DMF)]n·0.5(DMF)n (1), [Cu(hfipbb)(DEF)]n (2), [Cu3(hfipbb)3(DMA)3]n·6(DMA)n·2(H2O)n (3), and [Cu2(hfipbb)2(DEA)2]n·2(DEA)n·2(H2O)n (4), have been synthesized where hfipbb = 4,4'-(hexafluoroisopropylidene)bis(benzoate), DMF = N,N'-dimethylformamide, DEF = N,N'-diethylformamide, DMA = N,N'-dimethylacetamide, and DEA = N,N'-diethylacetamide. The choice of either a formamide or acetamide solvent ligand leads to a 2D, doubly interpenetrated (1 and 2) or noninterpenetrated (3 and 4) MOF structure. Despite their lower potential void spaces, the doubly interpenetrated structures have superior carbon dioxide and hydrogen sorption properties. Their 195 K CO2 sorption isotherms display inflection points, followed by ∼3-fold increases in their sorption capacities and very large extents of hysteretic behavior. This shows that small changes in the identity of the ligated solvent ligand can affect whether the resulting MOF is interpenetrated or noninterpenetrated and so drastically affect the sorption properties. In addition, the activated phase of a fifth MOF, synthesized through DMF ligand exchange with water in 1 (1W), does not display an inflection point and subsequent increased CO2 sorption at 195 K, despite having the same degree of interpenetration, showing that even more subtle differences in the desolvated phases can lead to marked differences in their sorption behavior.