A question about cooperation

With a friend, we like to play in cooperation : we summoned each other to pass all areas and bosses, for the fun of it. Of course, we are at almost the same SL. Usually it work perfectly well. But at some point, he entered the dark moon covenant and I entered the darkwraith one. We realize then that we never see each other sign. As soon as I changed for the dark moon cov, it was possible again.
So it's not possible to summon if one is in the darkmoon and the other in the darkwraith ? Or it was just bad luck and we should wait much longer ? (usually his or my sign appears rather quiclky, like less than one minute).

Iirc, the game tends to prefer pairing people who are of the same covenant. At least this is true for the Way of the White and the Princess' Guard. Perhaps that played a role.