If you make a character global, the default dialog system doesn't work automatically, you need to implement it yourself. Don't worry, it is very simple. Go into the story editor and create a new goal, called start or something. In the INIT, write something like this.
PartyMembers(CHARACTER_Player1);
PartyMembers(CHARACTER_Player2);
PartyMembers is just property that is true or false for the character, you can call it whatever you want (unless something is already called that or a PROC has the same name).
Now, make a new goal, call it Global_Dialog or something. In the KB section add this code.
// Party member speaking to NPC
// ---------------------------------------------------------------------------------
IF DialogStartRequested(_Char, _Player)
AND NOT PartyMembers(_Char)
AND PartyMembers(_Player)
AND CharacterIsDead(_Char,0)
THEN StartDefaultDialog(_Char, _Player);
This will make so when you click on a character for dialog, it will check if the dialog is between a player and a npc and whether or not you are trying to talk to a dead guy. If you are not trying to talk to a dead guy, it will start the default dialog that you define using the side menu when selecting a character.