A composite is a material in which two distinct constituents are discernible at the microscopic or mesoscopic scale. A familiar example is represented by layered materials such as plywood, but much more sophisticated examples appear in nature or are produced by modern techniques of additive manufacturing. Since each of the constituents is a material in its own right, it should not be surprising that for a binary composite a double groupoid arises naturally as a faithful mathematical representation of its local and distant symmetries. Even if the two constituents happen to be individually uniform, the composite may not be so. In this case, one says that the composite is misaligned or that it contains a distribution of defects. This circumstance can be quantified in terms of the properties of the double groupoid.