The internal organization of cells is largely determined by the architecture and orientation of the microtubule network. Microtubules serve as polar tracks for the selective transport of specific molecular motors toward either their plus or minus ends. How both motors reciprocally move microtubules and organize the network’s arrangement and polarity is unknown. Here, we combined experiments on reconstituted systems and theory to study the interaction of microtubules with both plus- and minus-end directed motors bound to a fluid membrane. Depending on motor concentrations, the system could lead either to the constant transport of microtubules or to their alignment, stacking, and immobilization in regular bands that separate motors into domains of opposite polarities. In bands, microtubules shared the same polarity and segregated the two opposing motors accordingly. These regular patterns resulted from the balance of forces produced by the two motors as they walked in opposite directions along microtubules. The system was maintained in a dynamic steady state in which the directional transport of microtubule-bound motors compensates for the random diffusion of lipid-bound motors. The size of motor domains depended on their respective concentrations. The constant flow of motors allowed the system to respond to variations in motor concentrations by moving microtubules to adapt to the new force balance. The polar sorting and linear arrangement of microtubules associated with the segregation of motors of opposite polarity are typical of cellular architectures, which these data may help to better understand.