Given obstacles and crossing areas together with two pairs of terminals on the plane, our algorithm finds a pair of rectilinear paths which connect the pairs of terminals, neither pass through any obstacle nor cross each other except in the crossing areas, and minimize the total length, where all obstacles and crossing areas are assumed to be axis-parallel rectangles. The algorithm takes O(n log n) time and O(n) space, where n is the total number of obstacles and crossing areas.