Edit: Think i misunderstood you. If one player initiates dialogue with an npc, then you don't both get the dialogue tree unless they are special npcs. If that was your issue then yes that's the way it is sadly. Which means you both have to talk to npcs if you both want to get everything. It should show up as floating text over the character speaking however. BUt it is way less convenient than say old crpg games like baldur's gate, where both would see the dialogue on one screen.
I suggest doing what we do, read the text out loud on skype/vent etc. However that can be very tiresome as it is a text heavy game.
Another option is reading the dialog log on the bottom right- everything anyone says is written there.