var chat1 = "A:How are you?B:I'm fine, thanks.";
var chat2 = "A:How are you?";

var c1 = chat1.match(/b(A:)(.*?)(B:)(.*?)b/i);
// c1[1] daria "A:", c1[2] daria "How are you?", c1[3] daria "B:" e c1[4] daria "I'm fine, thanks."
var c2 = chat2.match(/b(A:)(.*?)b/i);
// c2[1] daria "A:", c2[2] daria "How are you?"

console.log(c1);
// Resultado:
Array [ "A:How are you?B:", "A:", "How are you?", "B:", "" ]

console.log(c2);
// Resultado:
Array [ "A:", "A:", "" ]