Inverse lithography mask design and double-exposure lithography are two technologies that have gained a lot of attention in the recent past. Inverse lithography consists of synthesizing the input mask that leads to the desired output wafer pattern by inverting the mathematical forward model from mask to wafer. Double-exposure lithography uses two pairs of mask and exposure to print a single (desired) wafer pattern. It usually involves splitting the latter into two parts. In this work, we present some preliminary results in our unique effort to combine the previous two powerful techniques. The goal is to use the inverse imaging approach to automatically synthesize the masks required to print the desired wafer pattern employing double-exposure lithography. We employ the pixel-based mask representation, analytically calculate the gradient, and use a cyclic coordinate descent optimization algorithm to synthesize the two masks. We present results for chromeless phase-shift masks for an idealized case of a coherent imaging system using the Kirchhoff approximation. The results indicate that our algorithm automatically splits the target pattern into two (overlapping) parts, which are used separately during the individual exposures. Furthermore, the proposed approach is also capable of resolving the phase conflicts. The comparison with a single-exposure case indicates a superior contrast and no hot-spots.