Maps with properly bicolored faces can be understood as a special case of the 2-matrix model, or, equivalently, of the Ising model on maps. They already contain a complexity that is not present in general maps, as, when one wants to enumerate bicolored maps with a boundary, arises the question: which boundary condition to choose? Apart from the simplest and most well-known monochromatic condition, and its close sibling the Dobrushin one, others also appear naturally in models of random maps, such as the alternating condition. In this talk, after having introduced the objects and notions at play, I will show how the study of these different boundary conditions yields similar asymptotic behaviors, and uncovers unforeseen underlying structures. This is based on joint work with Jérémie Bouttier, and ongoing work with Valentin Baillard and Bertrand Eynard.