Having been introduced, Henry and Catherine dance but don't have much of an opportunity to talk until they sit down for tea. I really enjoy this first conversation between the two of them. I feel Catherine does pretty well considering it is probably her first grownup interaction with a man, certainly a worldly one. She easily gets into the swing of his humorous nod to 'new acquaintance' conversation. (She isn't sure if it's correct for her to laugh, though.)
From this initial conversation we see that Henry is charming, humorous, knowledgeable about women and accommodating. In fact his patience at listening to Mrs. Allen go on and on about muslins is used to show an important characteristic when Catherine "feared, as she listened to their discourse, that he indulged himself a little too much with the foibles of others." Her face must have revealed her concentrated reflections prompting him to ask her what she was thinking of so earnestly. She blushes and tells him she wasn't thinking of anything. His reply is, "That is artful and deep, to be sure, but I'd rather be told at once that you will not tell me." This shows that honesty/being honorable is important to him.