We report here an investigation of graphene field-effect transistors (G-FETs) in which the graphene channel is in contact with an electrolyte phase. In this work an ion gel, a mixture of poly(styrene-b-methyl methacrylate-b-styrene) triblock copolymer and ionic liquid 1-ethyl-3-methylimidazolium bis-(trifluoromethylsulfonyl)amide ([EMI][TFSA]), was employed as the electrolyte phase to simplify the device structure by eliminating the needs of electrolyte container and passivation layer that isolates metal contact from the electrolyte. The introduction of the electrolyte phase has an important advantage for fundamental measurements—the Fermi-level position EF of the graphene channel can be tracked by measuring its electrochemical potential with respect to a reference electrode immersed in the electrolyte phase. Thus, the potential δ required to fill the energy band of graphene with charge carriers (i.e., electrons or holes) can be directly measured from the electrochemical potential change while the carrier density in the graphene channel is independently controlled with back-gate bias. In turn, the quantum capacitance CQ (i.e., the DOS) of graphene can be estimated from this information. Furthermore, when the carriers in the graphene channel are induced through the electrolyte-gate (i.e., the counter electrode immersed in the electrolyte phase), the potential ΔΦEDL required to charge the electric double-layer at the graphene/electrolyte interface can be conveniently separated from δ by comparing electrochemical potentials of graphene during back- and electrolyte-gating. As we will show, our dual gated devices allow systematic determination of four parameters — δ, CQ, ΔΦEDL, and double layer capacitance CEDL — for graphene. The dual gated devices are generally useful testbeds for understanding transport and electronic structure, and the approaches we follow here should also be applicable for investigating other 2D materials such as MoS2 and ultrathin layers of conventional semiconductors.