No, it is not correct to say that each object is moving at the speed of light relative to each other. According to Einstein's theory of special relativity, the speed of light in a vacuum is always constant and the same for all observers, regardless of their relative motion. This means that no object with mass can reach or exceed the speed of light.
When two objects are moving in opposite directions at speeds close to the speed of light, their relative velocities do not simply add up. Instead, their velocities combine according to a relativistic formula known as the velocity addition formula. This formula takes into account the effects of time dilation and length contraction at high speeds.
As a result, even if two objects are moving away from each other at speeds that are each half the speed of light, their relative velocity, as measured by an observer in one of the objects, will be less than the speed of light. The exact calculation of the relative velocity would require applying the velocity addition formula, which takes into account the effects of relativistic motion.