The electrical double-layer interaction between two long, parallel rodlike objects partially immersed in a water/oil interface is analyzed. The present approach is applicable to a system containing two different objects. A family of shapes formed by deforming a cylinder is considered through a conformal mapping technique. An analytical expression for the electrical potential distribution for the system under consideration is derived under the Debye-Huckle condition. We show that the thicker the electrical double layer, the greater the interaction free energy and the stabler the system. For a fixed thickness of electrical double layer, the closer the objects to cylinders and/or the smaller the contact angle (the larger the fraction of an object in the water phase), the stable the system. Also, the greater the difference in the charged conditions on the two interaction objects, the stabler the system. If the deviation in the contact angle is close to pi/2, the interaction free energy is roughly a linear function of the position of the water/oil interface.