Rose did her best to smile, but seeing him like this in person was completely different from just speaking to him over the Network. Rose was certainly worried about him, and the way he was behaving now scared her. When he mentioned River, she opened her mouth slightly, of course he wouldn't remember that Rose and River have gotten to know each other after River's arrival.
Rose stared at River, doing her best to send an unspoken message to her. She smiled brightly at her. "Hello. It's nice to meet you." Rose had known the Doctor was married from her time at Mount Weather, so it wasn't a complete surprise to her. Her comfortableness came from being worried about the Doctor's current state.
Her head whipped back as he spoke again. "What do you mean not much time left?" Her eyes narrowed at him with concern. "Come on now, don't be like that. You're sticking around here, with us."