Fundamental measure theory (FMT) is an approximate non-perturbative density func- tional theory (DFT) [41], originally proposed by Rosenfeld for additive hard sphere mixtures [42, 43]. The approach was later generalised to other convex shapes [44, 45], which led to subsequent work [46, 47]. The bulk I - N coexistence densities (scaled by the cube of the platelet radius) and nematic order parameter at the transition ( c$_{I}$, c$_{N}$ and S$_{N}$ , respectively) were calculated by Frenkel and Eppenga in Ref. [20] by simulation; for more recent sim- ulation results see Ref. [48]. The values previously obtained from FMT are c$_{I}$ = 0 . 418, c$_{N}$ = 0 . 46 and S$_{N}$ = 0 . 53 [48], which are in agreement with the present study. Recently [49] these values were improved using the same method but with increased resolution to c$_{I}$ = 0 . 419, c$_{N}$ = 0 . 469 and S$_{N}$ = 0 . 533 [50]. The FMT functional for pure platelets was later utilised to study inhomogeneous situations including the I - N interface and wetting at a hard wall [25, 51] and capillary nematisation of platelets between two parallel walls [48]. Generalising the theory for the corresponding one-component system [52], we here propose a functional to describe binary mixtures of vanishingly thin circular platelets. Our theory features the exact virial second order term in density and an approximate term of third order in density. We investigate three types of demixing phase behaviour in the case of binary platelets with varying size ratio, finding I - N and N - N phase coexistence. We do not find stable I - I demixing (as could be driven by the depletion effect [53]) for the regimes considered in the present work. We restrict our attention to uniaxial arrangements of the (uniaxial) platelets, as we do not expect biaxial arrangement of the particles to occur. We study a range of size ratios in this investigation, ranging between λ = 1 . 1 and 5. We present the phase diagrams in different representations to facilitate comparison with simulations which may be performed in different ensembles or experiments. We expect the phase diagrams from FMT to be quantitatively more accurate than those from Onsager theory, which we calculate as a reference. The topologies of the phase diagrams are the same in both theories for our chosen values of the size ratio between two species. Although the integral kernel, which represents the pair excluded volume term, is the same for long thin rods as it is for platelets of vanishing thickness, the results from Onsager theory cannot be obtained by simple scaling of literature results for binary mixtures of rods. This paper is organised as follows. In Sec. II we define the model, outline the density functional theory and the conditions for thermodynamic stability and phase coexistence. In Sec. III we present results for the phase behaviour of binary platelet mixtures. In Sec. IV 4